Marquez, who turned 21 on Monday, sustained the injury on Wednesday during a dirt-track training session in Lleida, near Barcelona and close to his home town of Cervera, and has already started his rehabilitation.
The Spaniard will miss next week's test in Sepang, Malaysia, and possibly the one the following week at Phillip Island, Australia but is expected to have recovered in time to race in the season-opening grand prix in Qatar on March 23.
"The results showed no ligament damage or dislocation and no need to proceed with surgery," the doctor who treated Marquez, Xavier Mir, said in a statement.
"I expect he will need 3-4 weeks to fully recover."
Marquez, who became the youngest ever world champion last season in his rookie year, added: "It was a really unfortunate accident that could happen to anyone at any time.
"I was rushed to hospital and Dr. Mir treated me, thankfully there was no ligament damage and it seems like a clean break."