The Nerazzurri boss is concerned the Serbian could come back to haunt his former club as the Italian himself prepares to face his old employers
The former Serbia boss replaced Delio Rossi at the beleaguered Genoese club last week and got his reign underway with a 1-1 draw against Lazio on Sunday.
Lorik Cana struck in the 94th minute to deny Mihajlovic a dream start at the Stadio Luigi Ferraris and Mazzarri fears a backlash against his fourth-placed Inter side when they clash at San Siro on Sunday.
"So far I've seen a little, I’ll study him more carefully these days," Mazzarri, who used to coach the Blucerchiati, told Il Secolo XIX.
"The team seems to already be in good shape when you look at the players and now with Mihajlovic the team will have more fighting spirit.
"After a change of coach there is always a reaction and for us it's the worst time to meet them."
Mazzarri looked back on his time at Sampdoria fondly, but insisted he would not be doing his old side any favours, with Inter potentially able to overtake another of the 52-year-old's former clubs, Napoli, into third with victory.
"The two seasons I spent in Sampdoria were exciting," he added. "We played well and achieved important goals. With a little luck, we would have won more.
"Inter is my present and I have brought my professionalism here. Today, I am an opponent, even if it feels strange."