Girgenti said he met Kardashian in 2008 on a photo shoot and they struck up a relationship over text. The relationship turned sexual in 2009 when the reality star allegedly told him she was "on the outs" with her boyfriend Scott Disick.
Lawsuit documents obtained by TMZ said Mason was born nine months after Girgenti and Kardashian had unprotected sex.
The model said Mason resembles himself and the tot and his sister Penelope look nothing alike.
Kardashian's lawyer Shawn Chapman Holley sent a letter to Girgenti saying his allegations are "false and defamatory," the Los Angeles Times reported. Kardashian lawyer Todd Wilson told TMZ that Disick is Mason's father and Girgenti "has been selling false and fabricated stories to the tabloids for years."
"His claims are absurd and this is simply another shameful attempt to gain publicity and profit from fictional stories about my client," Wilson said.
A hearing was scheduled for next month, the Times reported.
Celebrity Families of 2014 [PHOTOS]