The 1963–64 season was the 62nd season in which Dundee competed at a Scottish national level, playing in Division One, where the club would finish in 6th place.

[2] They would be knocked out of the Quarter-finals of the League Cup by Hibernian, and made it to the final of the Scottish Cup, where they lost Rangers.

They would also compete in the revamped Summer Cup, being knocked out in the group stages.

Striker Alan Gilzean would break the club record for most goals in a single season, scoring 52 times in 48 appearances.

Statistics provided by Dee Archive.