The Belgium international was withdrawn due to the problem shortly after coming on as a substitute in Napoli's 1-0 defeat to Fiorentina on Sunday.
An MRI scan on Monday revealed the 26-year-old will miss Wednesday's trip to Catania as he undergoes physiotherapy and rehabilitation treatment on his right ankle.
Despite Sunday's loss to fourth-placed Fiorentina, Napoli enjoy a seven-point cushion in third and look set to clinch the final UEFA Champions League spot in Serie A.
However, coach Rafael Benitez will be eager for Mertens to return as soon as possible due as they continue with a tricky run of fixtures.
After their trip to Catania, Napoli host runaway leaders Juventus on Sunday before clashes with Parma and Lazio - who sit fifth and seventh respectively in the table.
Mertens, who joined Napoli from PSV last June, has featured 26 times in Serie A this term, scoring six times.
