The 20-year-old was forced off three minutes before half-time in the 1-1 draw at Underhill after injuring his knee making a challenge.
But boss Neal Ardley confirmed afterwards that Meades, on loan from Bournemouth, is expected to return to training this week.
Ardley will also hope to welcome back captain Steven Gregory for the visit of Rotherham on Saturday.
Midfielder Gregory, another player on loan from Dean Court, missed the clash against the Bees due to illness.
Stacy Long's late equaliser secured a valuable point for the Dons against their fellow strugglers and Ardley was delighted to give the club's fans something to shout about.
"I wouldn't say that I was impressed with our tenacity as that has to be demanded now every week," he said.
"If I was a fan on a cold day at Barnet the least I would expect is for the players to throw themselves into everything.
"Last week (at MK Dons) the supporters were phenomenal and they were brilliant again in turning out in their droves.
"I am just pleased that we gave them a performance that at least showed we were prepared to scrap and battle."