The copy of the book was not signed by Trump. Photos from the AP showed Rodman sporting a blazer on top of a pink shirt as well as his trademark facial piercings, handing over the book to the minister, Kim Il Guk.
Rodman has been visiting North Korea since Tuesday, his latest trip to the isolated state.
On that day, the North released American student Otto Warmbier who had been held for 17 months and was said by his parents to be in a coma.
Rodman visited the North in 2013 and 2014. The US government has issued travel warnings to Americans against travel to the North.
Rodman met North Korean Olympic athletes, including judo gold medalist An Kum Ae, reported the AP, which has a bureau in North Korea's capital of Pyongyang.
"All of you guys should be proud of yourselves, because, you know, a lot of people don’t give you guys credit, because this is such a small country, and not many people from North Korea can compete around the world,” Rodman was quoted as telling the athletes.
"But for you guys to come back here in your country, with a medal, that says a lot about North Korea, because people don’t really take North Korea so seriously about sports or anything like that."
The former basketball star has said his visit is not linked to the White House. Before Trump became president, Rodman appeared twice on his "Celebrity Apprentice" show and praised the billionaire real estate developer on Twitter during last year's election campaign.
Tension has escalated on the Korean peninsula over North Korea's nuclear and missile tests since last year.
North Korea has vowed to develop a nuclear-tipped missile capable of hitting the US mainland.
