Images have been circulating online of a Sheffield Wednesday fan typing “Where’s Baldock” on his phone and showing it to Sheffield United fans.
A spokesperson for Sheffield Wednesday said: “The club roundly condemn this abhorrent act.
“There is no place in football or society for such appalling behaviour.”
Baldock was found dead in a swimming pool at his home in Greece last month, aged just 31. He had played for Sheffield United for seven years.
Public outrage has been sparked, with some social media users calling for the fan to face a lifetime ban.
The Steel City derby took place for the first time in almost six years last weekend.
The game was held at Sheffield United’s Bramall Lane stadium. Kick off was pushed back to 12.30 to allow for the city’s Remembrance service to take place from 10.30am.
The club announced on the evening of the match that they are working with South Yorkshire Police on this matter.