"He also stayed overseas without a valid exit permit", the official added.
"Mr Kwan is therefore wanted for defaulting on his NS obligations", the ministry said in a statement.
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 Singaporean citizens are required to spend two years, in most cases, in a uniformed service as young adults. He reportedly applied twice to renounce his citizenship at a later date, but was rejected as he had not served in the military.
Kwan's publicist has not yet responded to a CNN request for comment.
Kwan left Singapore at age 11, first moving to Texas with his family, and has lived in the United States since then, Singapore media said.
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The film had its Singapore premiere on Tuesday night ahead of local release on Wednesday but Kwan was not among the cast or crew in attendance.
"Crazy Rich Asians" was adapted from the novel by Kevin Kwan. With a target on her back, she has to fend off catty socialites and hold her own against Nick's domineering mother (Michelle Yeoh) while remaining true to herself.
And like clockwork, one week after the film's release, The Hollywood Reporter let loose the news that Warner Brothers has officially moved forward on development of the second book in the Crazy Rich Asians trilogy, China Rich Girlfriend.
Shot nearly entirely in Singapore, plot of the book and film make good use of Kwan's homeland - coming across as "a love letter to the food, culture and beauty of this area", according to the film's producer, Brad Simpson.
The event took place at Capitol Theatre, one of Singapore's historic venues, and also attracted a bunch of local celebrities and the city's movers and shakers.