The wicket-keeper damaged a wrist in the recent T20 defeat against Yorkshire at Headingley, and has missed the past two matches, the first against Durham in the Blast and also the LV= Insurance County Championship date with Yorkshire.
Rossington underwent a scan on the problem at the beginning of the week, and although he will miss the Lightning T20 date as well as the Championship clash with Glamorgan in Cardiff, he should be quickly back in action.
"Adam has had the result from a scan, and he is not going to be playing for probably another 10 days or so," revealed head coach David Ripley
"It was an impact injury from Headingley, but it has come out as some kind of issue with his wrist.
"He has been in a lot of pain and we didn't quite know what it was, so at least we now know and it is nothing that is going to ruin his season or anything like that.
"But it does mean that he is unavailable for Friday night and for Cardiff for sure, and we will then see where we are by the time we get to the Derbyshire game and then Birmingham in those last two T20s.
"Fingers crossed, he might be able to feature."
The Steelbacks are due to host Derbyshire on Friday, July 16, before going to Edgbaston on Sunday, July 18.
Overseas all-rounder Wayne Parnell is also struggling with an injury and looks set to be rested for the four-day match in south Wales, but could yet feature in the Blast on Friday.
"Wayne has picked up an ankle injury in the game against Yorkshire," said Ripley.
"We hope he will be okay for Friday, but I imagine that at this stage another four day game would be a bit of a push, especially now as we are not aiming for the big prize down at Cardiff.
"I think it would be silly for us to risk him, but other than those two we are pretty much all good."
Once the T20 group stages are completed, Rossington will be away from Northants for a month as he takes up his place in the London Spirit squad for the new Hundred competition.
That means the red ball skipper will miss the Royal London One Day Cup campaign, as will fellow Hundred players Josh Cobb and Brandon Glover, who are playing for Welsh Fire and Oval Invincibles respectively, and Ripley himself, who is assistant to Shane Warne at the Spirit.