The 23-year-old started the match against the U’s after a six-week lay-off with a hamstring problem picked up in the 3-0 loss to Port Vale.
Lasting just 35 minutes on Monday, Browne will be ruled out for the final two games of the season to see his campaign come to a stop-start end having made just 13 appearances since the turn of the year.
Commenting, Interim Manager Neale Marmon told YTFC.net: “We knew it would be a risk with Rhys and we took the risk, but we’re sorry to the boy that he’ll now be out for four or five weeks.”
Town’s number seven will join defender Gary Warren in playing no further part in 2018/19, although Ryan Seager could be back in contention at Northampton this weekend.
The striker picked up a knee injury in the latter stages of Good Friday’s defeat at Crewe Alexandra and missed Monday’s action at Huish Park.
Commenting on Seager’s potential involvement and the squad’s general fitness, Marmon added:
“He did a bit of a programme this morning (Wednesday) but he’s not fit enough to get really properly involved at the moment, but I believe by Friday he should be available.
“It’s normal that when you get a result, the players are always raring to go again so we had the whole squad training apart from Gary Warren, Rhys Browne and Josh Grant.”