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."
Source: PA