Wright picked up the injury against League Two leaders Northampton Town on Tuesday and was replaced by Chey Dunkley for the final 14 minutes.
"It looks like a grade one tear to his hamstring, which rules him out for around 10 days to start with," manager Michael Appleton told BBC Radio Oxford.
"It's a blow from a playing point of view and also because he's a leader."
Wright, 29, has made 30 appearances in all competitions for Oxford this season.
On Saturday they host fourth-placed Accrington, who are six points behind Appleton's side with two games in hand.
Oxford United captain Jake Wright is set to be out for three to four games with a hamstring tear.