"Neser is not going to be available for the next three games. He's got some Australia commitments so we're not going to have him," Glamorgan's director of cricket, Mark Wallace, said.
"We've moved on a short-term contract to bring in Hatzoglou to give us some more bowling depth. Peter's got a good record around the world, mostly in the Big Bash, but in a few other franchise competitions as well.
"We're really looking forward to adding him to the Glamorgan squad and hopefully kickstarting this T20 campaign."
Hatzoglou, a two-time Big Bash winner with Perth Scorchers, featured for Oval Invincibles in the Hundred last summer and has also played in the Pakistan Super League.
"I'm really excited to make an impact during my stay here," Hatzoglou said. "With Neser being called up to the Australian squad, I wasn't too far away in Essex and I guess I got the tap on the shoulder for the call up which is great.
"It's been really good to have some success with the Perth Scorchers over the last couple of years. I had some experience in the Hundred last year playing for the Oval Invincibles and I'm sure it'll be a nice little transition into the Blast this year."