The former Liverpool defender played under Benitez at Anfield between 2004 and 2010 and won the Champions League in 2005 and FA Cup in 2006, but he does not expect his former boss to spend a similarly long time at St James' Park.
The Spaniard guided Newcastle to promotion from the Championship after taking over in 2016, but Carragher thinks a damaged relationship with owner Mike Ashley over transfers is likely to result in him walking away.
On 'Monday Night Football', Carragher said: "If I'm being totally honest, I don't expect to see Rafa Benitez at Newcastle over a sustained, long period of time.
"I think eventually something will happen with him and the owner and unfortunately for Newcastle this is not going to be a happy and long marriage.
"So enjoy it while he's here."
Carragher expects Newcastle to avoid relegation but does not think his former boss will be able to secure a top-half finish given the lack of investment in the squad over the summer.
He said: "You can't turn Newcastle into a force if you're buying players like Joselu, who was a squad player at Stoke who Newcastle are probably going to rival this season, maybe in the bottom half of the table.
"I don't think there's any chance of Newcastle going down, just because of the manager. He is very pragmatic and he'll make it very difficult.
"I don't think Liverpool have got an easy game going to St James' at the weekend. You saw how they were against Tottenham before they went down to 10 men.
"In every game Newcastle have, you'll very rarely see them lose 4-0 or 5-0, as you might see teams in the bottom half of the table.
"I think that's where Newcastle will be, but I don't expect to see them in a relegation fight."