The Colombia international pulled up with the problem during a friendly against Red Star Belgrade over the weekend.
Muriel subsequently underwent tests on Tuesday that indicated a tear in his right thigh.
Udinese have now confirmed that the 23-year-old is to undergo further evaluation in eight to 10 days to get a clearer picture as to the extent of the issue.
"[Muriel] has already started physiotherapy as appropriate," read a statement on Udinese's website.
"In eight to 10 days he will have repeated examinations which will better enable us to define a more precise prognosis."
Muriel has made 11 Serie A appearances this season for an Udinese side that sit eighth in Italy's top flight.