Osimhen and Politano were both sent off in last weekend's 2-0 defeat at AS Roma. Stanislav Lobotka went off injured in that game and another midfielder, Jesper Lindstrom, missed that game through injury and both are doubtful for the Monza match.
"We're in quite an emergency, I've even made a list," Mazzarri told a press conference on Thursday.
"Lobotka is a first choice, if he's fit he will play. If he doesn't make it I have great confidence in (Jens) Cajuste, who will become very strong.
"Lindstrom, even if he's fit, doesn't have ninety minutes in him, and so will either start or come on from the bench."
Brazilian defender Natan came on late in the game with Roma, and despite suffering a shoulder injury, remained on the pitch with Napoli already down to nine men.
"The doctor told me that it will take a month and a half, so he won't be back for now," Mazzarri confirmed.
The manager also announced an injury to Diego Demme, and although Eljif Elmas signed for Red Bull Leipzig on Wednesday, the manager is not expecting too much from the upcoming transfer window.
"I'm not expecting a revolution because you don't and can't do it in January.
"You know very well that I prefer the club to talk about the market, I want to help the players regain the confidence of last year."
With both Osimhen and Politano suspended, Mazzarri must choose between Giovanni Simeone or Giacomo Raspadori for Friday's game with Monza.
"Making them play together would mean making a big change to the formation and in any case you need to have a striker on the bench," Mazzarri said.
"We'll see who will start and who will come on during the game."
Since Osimhen returned from a hamstring injury, the Nigerian has scored just once in five league games, and his sending off against Roma was a disappointing way to end his time with Napoli before leaving to join the national team.
Osimhen will join the Nigeria squad for the African Cup of Nations finals in January.
"Since he came back, he has been battered even when the ball is far away," Mazzarri said.
"Maybe he felt the responsibility after such a great campaign last season, it can happen to make mistakes when nervous. Unfortunately he was back from injury and now there's the African Cup of Nations.
"I forgive him, not because I'm a good guy but because he needs to be protected."
Napoli are seventh in the standings with 27 points, one point behind Roma in sixth, while Monza are 11th on 21 points.
