The Bantams have opted to take up a 24-hour recall clause in the deal to bring Muirhead back into their squad.
Bradford caretaker boss David Wetherall wants him available for the final four games of the season as they aim to fight off relegation.
The 24-year-old has not figured for Bradford since 1 January but scored three times in 12 starts for Rochdale since joining them in mid-February.
"I'm disappointed yes, but with the play-offs now out of reach I suppose I'm not as disappointed as I could have been," Dale boss Keith Hill told his club's website.