Phillip and Evelyn Bradley were arrested on Monday (19Nov12) by detectives in Winter Haven, Florida.
The couple allegedly used the Starships hitmaker's name to borrow $36,000 (£22,500) from investors in order to finance the gig, which was supposed to take place at Simmers-Young Park on 24 October (12).
Police became suspicious and they launched an investigation after contacting representatives for both performers.
A rep for Minaj told the investigators the star would be touring outside of the country at the time and Drake's agent said the rapper would be attending his birthday party in Las Vegas.
Polk County sheriff's spokeswoman Carrie Eleazer says, "Immediately the investigative officers were like, 'This isn't right. There is no way these two performers are coming here. That doesn't sound legit (legitimate)'."
Sheriff Grady Judd adds, "We... contacted the management companies for both Nicki Minaj and Drake... And they said, 'She's out of the country' and the day of the event is Drake's birthday so he's going to be at a party in Las Vegas."
Phillip Bradley has been charged with one count of scheming to defraud, one count of grand theft of more than $100,000 (£62,500), and unlawful use of two-way communication.
Evelyn Bradley faces one count of scheming to defraud and one count of grand theft of more than $20,000 (£12,500).