The 21-year-old has made 10 starts in Serie A so far this season, three more than his total in the league last term, and has grown in confidence and stature under Rudi Garcia.
Initial reports from Italy suggested that Dodo would not return until April - despite Roma's refusal to give an official return date - but the former Corinthians defender hinted at a shorter spell on the sidelines.
"Four-to-five weeks out will be really hard, now so much therapy and rest," Dodo wrote on Twitter.
"Thank you for all of your messages, I hope to see you soon at the Stadio Olimpico."
The Brazilian is at least expected to miss key Giallorossi games such as Coppa Italia semifinal ties with Napoli, a home clash with Inter and a Rome derby with bitter rival Lazio.
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