- January 13: A mudslide kills 13 persons in Mikro Chorio, Evritania prefecture.
- January 24: Crown Prince Constantine of Greece and Princess Anna Maria of Denmark get engaged.
- February 5: Vassilis Georgiou begins his career as a sportscaster (Panathinaikos - Asteras 2-1 at Leoforos)
- February 21: The ERE government puts forward proposals to amend the Greek constitution by expanding the power of the executive branch of government.
- March 1: A fixed fine is established for Members of the Greek Parliament who miss a session without a valid excuse.
- April 20: Queen Frederika visits England where she will become the target of demonstrators.
- April 21: MP Gregoris Lambrakis marches alone in the Marathon to Athens peace rally that was banned by the police.
- May 8: St. Sevastopoulos breaks the 2m mark for a new Greek record in the high jump.
- May 17: Stjepan Bobek takes over as coach of Panathinaikos FC.
- May 18: French President, Charles De Gaulle, visits Greece and speaks in the Hellenic Parliament.
- May 22: MP Grigoris Lambrakis is run down by a delivery truck driven by two right-wing extremists (Emmanouil Emmanouilidis and Spyros Gotzamanis) after delivering the keynote speech at a pacifist meeting in Thessaloniki. He will die five days later.
- May 27: Grigoris Lambrakis, a leftist politician, succumbs to his injuries of May 22.
- May 28: Hundreds of thousands attend the funeral of murdered MP Grigoris Lambrakis.
- June 2: AEK defeat Iraklis 5-0 for the Greek League. All five goals are scored by Kostas Nestoridis.
- June 11: Constantine Karamanlis resigns the premiership after a disagreement with King Paul of Greece
- June 16: King Paul of Greece appoints Panagiotis Pipinelis as Prime Minster following Constantine Karamanlis' resignation
- June 23: AEK celebrate their first post-World War II championship as they draw 3-3 with Panathinaikos in a playoff game. Mimis Papaioannou (2) and Kostas Nestoridis score for the champions (the latter directly from a corner kick).
- July 1: Aristotle Onassis acquires Skorpios island off the coast of Lefkada.
- July 9: King Paul and Queen Frederika visit England where they are greeted by mass demonstrations.
- July 12: King Paul and Queen Frederika return from England where they were the target of mass demonstrations.
- July 25: Panathinaikos footballer, Panikos Shailos, is killed in an automobile accident in Athens. His passenger, team mate Kostas Linoxylakis, survives.
- September 18: Olympiakos defeat Levski Sofia 1-0 in Istanbul and are crowned Champions of the Balkans. Centre back Mimis Stefanakos headed home the winning goal in the 87th minute.
- September 18: AEK play their first match in Europe - a 7-2 loss to AS Monaco (78' Nestoridis, 80' Tasinos).
- September 29: Stylianos Mavromichalis forms a caretaker government.
- September 29: In a memorable football game, Panathinaikos defeat AEK 5-4 after trailing 0-2 and 1-3.
- October 20: Olympiakos defeat Zaglebie Sosnowiec of Poland 2-0 in Vienna for the Cupwinners' Cup and become the first club from Greece to advance to the next round of a European Cup.
- November 3: Georgios Papandreou's political party, Center Union, emerges the winner in the national elections held and forms a minority government with 42.2% of the votes.
- November 13: APOEL FC set a negative European record as they lose to Sporting Lisbon 16-1 in the first leg of the second round of the Cup Winners' Cup.
- November 25: Queen Frederica attends the funeral of US President John F. Kennedy on behalf of Greece.
- November 27: The players of PAOK walk off the pitch when the Bulgarian referee denies them an obvious penalty against Olympiakos. Olympiakos are awarded the match 2-0 (forfeit).
- November 27: Cyprus defeat Greece 3-1 in the first game ever played between the two teams. Mimis Papaioannou debuts with Greece.
- November 30: Archbishop Makarios III proposes 13 amendments to the constitution of Cyprus.
- December 3 : Prime Minister Georgios Papandreou announces the government's plan to distribute free books to all elementary and highschool students.
- December 9: Constantine Karamanlis resigns from the leadership of his party, National Radical Union (ERE), and leaves for an 11 year self-imposed exile to Paris, France.
- December 9: Athenian high society is shaken up by the murder of heiress Ioulia Syreggela by her Iranian lover Reza Abbaz Mirtolooi.
- December 10: The Nobel for Literature is awarded for the first time to a Greek; to George Seferis. In his award speech the poet is quoted as saying: "I belong to a small country. Our place is small but it has a huge tradition... The Greek language has never stopped being spoken..."
- December 21: The Cyprus crisis of 1963-1964 begins with a firefight in Nicosia that leaves one Greek Cypriot policeman and two Turkish Cypriot civilians dead.
- December 27: Student rallies take place in Athens and Thessaloniki in favor of a union between Greece and Cyprus.
- December 30: Banker Ioannis Paraskevopoulos forms a caretaker government as elections are proclaimed for February 1964.
- December 30: The Green Line, separating the Greek and Turkish sectors of Lefkosia, is agreed upon by the two communities.
- March 3: Sophia Aliberti, actress
- March 8: Juan Gilberto Funes, played for Olympiakos in the late 1980s.
- June 14: Toni Savevski, football player and coach
- June 15: Daniil Papadopoulos, footballer
- June 25: George Michael, Cypriot-British singer