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.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.