Kinsella limped off towards the end of the 2-1 defeat and will have the procedure in the coming days.
Saddlers boss Matt Taylor hopes the 25-year-old midfielder will be on the sidelines 'for weeks as opposed to months'.
"Liam got injured during the game against Newport, and you know it's always more sinister when there's no-one near you," said Taylor.
"That was the case with Liam, unfortunately.
"He's got a problem with his knee, so he's going to undergo a procedure in the next four or five days. We'll know a bit more after that.
"I think it'll be weeks as opposed to months.
"That's what we're led to believe. That's the information we've been given from the consultant.
"It's difficult as Liam has been performing consistently, but what it does do is give other members of the squad an opportunity."
Kinsella joins Conor Wilkinson (hamstring) and Rory Holden (knee) on the injury list for Walsall.
Joss Labadie will also miss the Saddlers' clash with Bristol Rovers on Saturday through suspension.
Taylor added: "Liam is devastated, as are all of us.
"But at the moment, it could've been a lot worse.
"I know he'll do everything he possibly can to be back fit as quick as humanly possible."