Rodman was roundly criticised for his angry tirade in an interview with CNN, in which he appeared to suggest that the missionary, Kenneth Bae, had merited the prison sentence of 15 years handed down last year.
"I want to first apologise to Kenneth Bae's family," Rodman said in a statement released Thursday by his publicist and cited by CNN.
"I embarrassed a lot of people," said Rodman, who was in the North Korean capital for an exhibition basketball match he had organised to mark the birthday of North Korean leader Kim Jong-Un.
"I'm very sorry. At this point I should know better than to make political statements. I'm truly sorry."
Rodman's trip to North Korea along with a handful of other former NBA players has courted controversy, with accusations of pandering to a totalitarian regime with a terrible record on human rights.
At the exhibition match on Wednesday, Rodman had sung Happy Birthday to his "best friend" Kim who was watching the game in a packed Pyongyang auditorium.
Kim just last month oversaw the execution of his powerful uncle and political mentor Jang Song-Thaek on charges of treason and corruption.
It was Rodman's fourth trip to North Korea in 12 months and he has been criticised for failing to raise human rights issues or the plight of Bae, whose family has voiced disgust at his television interview.
In his statement, Rodman said the day of the interview had been "very stressful."
"Some of my teammates were leaving because of pressure from their families and business associates," he said, adding that his dream of "basketball diplomacy was quickly falling apart."
"I had been drinking," he said. "It's not an excuse but by the time the interview happened I was upset. I was overwhelmed."
Bae, a 45-year-old tour operator, was arrested in November 2012 as he entered the northeastern North Korean port city of Rason.
North Korea described Bae as a Christian evangelist who smuggled inflammatory material into the country and sentenced him to 15 years' hard labor for allegedly seeking to topple the government.
Asked in the CNN interview if he would use his influence with Kim Jong-Un to make the case for Bae's release, Rodman had said: "I don't give a rat's ass what the hell you think."
Rodman played in the first half of Wednesday's exhibition game before changing out of his basketball gear and joining Kim in the stands where they chatted and smoked together.
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