Murphy, on loan from Norwich City, posted a picture of himself on the photo messaging site Snapchat accompanied by the caption: "We are going to lose...Again."
Blackpool are six points adrift at the bottom of the Championship (second tier) table and the joke was not appreciated by the club's fans.
"Jacob is a talented player with a bright future ahead of him and his recent actions should not detract from that," manager Lee Clark said on Blackpool's website on Wednesday.
"However, he realises that he made an error of judgement and understands why we have come to this decision.
"The players and the team need to be fully focussed on our fight to stay in the Championship."
Murphy apologised for his actions.
"I'd like to offer my sincerest apologies to the manager, my team mates, the fans and everybody at Blackpool Football Club for the hurt and embarrassment that a recent photo message I sent has caused," he said.
"It was totally unprofessional of me and a foolish thing to do," Murphy added.
(Reporting by Ed Osmond; Editing by Mark Lamport-Stokes)
