The pair, who helped Watford gain promotion to the Premier League in 2014-15, were reunited at Hillsborough on Tuesday, as Wednesday beat Derby 2-0.
Pudil met up with Vydra shortly after he helped to shut out the 18-goal striker, and wrote: "Rivals on a pitch but still friends after a game. Great to see you @matej20vydra #czechfriendscz.
Pudil and Vydra are not the only members of Watford's promotion winning squad to have since signed for Wednesday or Derby, after Almen Abdi and Fernando Forestieri [both Owls] and Ikechi Anya [Rams].
However, Anya was the only other to feature at Hillsborough on Tuesday, with both Abdi and Forestieri currently sidelined through injury.
Lucas Joao scored both goals for Sheffield Wednesday, who won for the first time in the league since Boxing Day and first time at home since Halloween.
The result meant Derby failed to return to the Championship's automatic positions, and they have now played a game more than second-placed Aston Villa, who lead them by a point.