Keane missed Ireland's Euro 2016 warm-up friendlies against Switzerland and Slovakia after picking up a knee injury against San Jose Earthquakes towards the end of March and subsequently underwent surgery to correct the issue.
“He needed it (surgery); he had some loose pieces in his knee and needed to have those removed. It’s a fairly normal [occurrence]," Arena told reporters.
"It’s cartilage and a lot of players have some type of issue with their knees at some point. He should be fine. I’d say in close to a month, he’ll be back to full speed."
As well as Keane, Ireland boss Martin O'Neill is also sweating over the fitness of Jonathan Walters, who also had surgery on his knee, while Southampton striker Shane Long sustained an injury in the 2-2 draw with Slovakia.
However, the news that Keane should be fit within a month will come as a boost to O'Neill, who will look to finalise his team's preparations for the European Championship in friendly games against the Netherlands and Belarus in May.