Kevin Kwan, who has lived in the US since he was 11 but is still a Singapore citizen, faces up to three years in jail and a hefty fine if convicted, the city-state's defence ministry said.
The movie adaption of his bestseller, which focuses on the glamorous world of Singapore's super-rich, was released in the United States last week and has been hailed as a watershed for Hollywood diversity due to its mostly Asian cast.
The film had its Singapore premiere Tuesday, with some of its stars gracing the red carpet and hundreds of fans turning out -- but Kwan was conspicuous by his absence, Singapore's Straits Times newspaper reported.
And in a twist worthy of a Hollywood thriller, Singapore's defence ministry revealed in a statement that Kwan "failed to register for National Service in 1990, despite notices and letters sent to his overseas address.
"He also stayed overseas without a valid exit permit."
The Singapore-American author had committed offences under the enlistment act and faces a fine of up to Sg$10,000 ($7,300) and a prison term of up to three years if convicted, the ministry said.
Male Singapore citizens are required to undergo two years of national service upon turning 18. They can either serve in the military, the police or the civil defence force.
The defence ministry said Kwan sought to renounce his Singapore citizenship in 1994, but his application and a subsequent appeal were rejected due to his failure to complete national service.
"Crazy Rich Asians", the first Hollywood film for a generation to have a majority-Asian cast, tells the tale of an Asian-American woman who is plunged into the world of Singapore's wealthy elite after travelling to the city with her boyfriend.
While it has been widely praised in the US, the movie has drawn flak in Singapore for focusing on the wealthy ethnic Chinese and ignoring the country's substantial minorities.