Papadakis began his club career with Panathinaikos, in 2015. He was loaned to Kolossos, prior to the 2016–17 Greek Basket League season. He spent three seasons there, appearing in 22, 24 and 35 games, respectively, and averaging around 2.4 points per game.
On August 11, 2020, Papadakis was once again loaned to Larisa.[1] With Larisa, Papadakis averaged 6.5 points, 1.9 rebounds, and 2.3 assists, playing 17.3 minutes per contest.
Papadakis spent the 2021-22 campaign with Iraklis and in 23 games, he averaged 7 points, 2.3 rebounds and 3.3 assists, shooting 33% from the 3-point line and playing around 23 minutes per contest.
On August 26, 2022, Papadakis signed a one-year contract with AEK Athens.[2] In 23 league games, he averaged 3 points, 1 rebound and 0.6 assists in 9 minutes per contest.
On August 1, 2023, Papadakis signed with Lavrio. On December 11, 2023, he returned to Kolossos Rodou in an unofficial trade for Costis Gontikas.