Meslier's 53rd-minute collision with Raúl Jiménez changed the face of the game at Molineux on Friday night.
Leeds were trailing Wolves by two goals when the Frenchman rushed out of his area to deny Jiménez a clear run on goal.
Meslier beat Jiménez to the ball but the pair, in their rush to win the footrace, came together with some force.
Referee Kevin Friend showed Jiménez, already on a caution, a yellow card and so the Mexican departed the field of play, leaving the home side to play the best part of the second half with ten players.
The Whites shot-stopper was in some discomfort after the collision and so was forced off the pitch. On the bench, Meslier joined Patrick Bamford, Mateusz Klich, and Diego Llorente - who had all been substituted with injuries before the break - to become United's fourth casualty of the game, while 21-year-old 'keeper Kristoffer Klaesson was called up to make his Premier League debut.
After the game, Leeds head coach Jesse Marsch said that Meslier had picked up a hip contusion, the seriousness of which would be revealed in the coming days.
On Saturday, Meslier took to Instagram to reassure fans about his injury.
"Thank you for all your messages!" Meslier wrote.
"I am doing well considering the circumstances.
"The comeback and the victory of the team make the pains less.
"I am in good hands and hope to be back on the pitch soon."