Dawson was stretchered off during England's 4-0 victory over Bulgaria on Friday night after his leg collapsed beneath him in a freak accident early in the second half.
Scans showed the 26-year-old defender had only sprained left knee ligaments and a left ankle ligament and he could be back in action by the end of next month.
"First of all, it's a big blow for Michael and a great shame for him," Redknapp told the club's official website, "but watching it live, I thought it could have been worse than it's turned out.
"It could have been his cruciate ligament and that would have been the end of the season for him but, as it is, it's not such a long job and he should be back in a couple of months."
Redknapp believes Dawson's injury has underlined the value of signing veteran former Arsenal defender William Gallas on a free transfer last month.
"Jonathan Woodgate is struggling, Ledley King can't play every game and you also have to remember that Michael had an Achilles injury last season, so it was always a position we needed to do something in and that's why we did it (signed Gallas)," Redknapp said.
"Sebastien Bassong was excellent last season and we've got decent cover in there, players who can come in and do a job, but you also need experience. Ledley's got experience, Michael's got experience and now William's experience will be invaluable.
"He'll give us a bit of know-how and a real presence. You don't do what he's done in the game without being a top, top player and he's got all the medals to show for it."