Barkley suffered a "personal injury" in the 17-11 Guinness Premiership victory at the Recreation Ground, but the 24-year-old centre should be available to face the All Blacks on November 5.
"Olly went in to make a tackle and a boot flicked up into his groin," Meehan said.
"He's got a personal injury there, and I don't think he'll be doing a lot of running around at the England training session next week."
Meehan was unable to give England coach Andy Robinson any further news on the progress of lock Steve Borthwick, who underwent minor surgery on his knee earlier this week.
"It's a question of waiting for the first two weeks because he can't do anything on it," Meehan said. "After that we'll see how he progresses."
In a scrappy game lacking any real quality, Meehan's men ran out deserved winners over a Worcester side that has yet to register a victory this season.
Alex Lutui's try deep into injury-time earned the visitors a bonus point after Nick Walshe had scored a 47th-minute try for Bath.
Meehan admitted it was a disappointing game. "The main objective was to win today and we did that, although we certainly didn't entertain anybody," he said.
"We didn't look after the ball as well as we should have and as a result we didn't flow."
Meehan's opposite man Anthony Eddy was frustrated by his side's lack of discipline after seeing captain Pat Sanderson and prop Chris Horsman sin-binned for killing the ball.
It was Horsman's third consecutive yellow card and could result in a ban being handed down by the RFU.
"It's extremely disappointing (the lack of discipline)," Eddy said.
"I'll have a look further at the game to see exactly what they were for so we can deal with it.
"We haven't hit panic stations or anything at this time. It would be nice to have a few more points on the table but they'll come as the season goes on."