Vick (13-1) publicly called for the bout on Wednesday, after ESPN reported Iaquinta (13-4-1) withdrew for undisclosed reasons. The UFC Fight Night event is scheduled to take place at Pinnacle Bank Arena.
"That punching bag Gaethje don't want these problems!!" Vick wrote on social media.
Gaethje (18-2) is a former WSOF champion, coming off back-to-back losses in the UFC to Eddie Alvarez and Dustin Poirier. He has built a reputation as one of the most entertaining fighters in the world.
Shortly after Iaquinta withdrew from the bout, Gaethje's manager Ali Abdelaziz told ESPN he was confident the UFC would find a replacement.
"UFC will find someone else to fight Justin, and it will be an exciting fight. It doesn't matter who fights Justin, it could be a chair in there, it will be exciting."
Vick, of Texas, has been calling for a highly ranked opponent. The 31-year-old holds a sterling record of 9-1 in the UFC.