Following his junior season, he was allowed to turn pro as a hardship case. Burden was drafted by the Virginia Squires of the American Basketball Association and the New York Knicks of the National Basketball Association. He chose Virginia, but left after one season, during which he had a serious argument with coach Bill Musselman. Upon joining the Knicks, he stated "In Virginia I saw the bad side of pro basketball, in New York I know I'll see the good side". In the 1976-77 season, Burden got into 61 games for the Knicks in a backup role, averaging 10 minutes and 5.7 points per game. However, in the 77-78 season Knicks coach Willis Reed became frustrated with Burden's lack of defensive play, and sent him to the disabled list for the remainder of the season after he played in just two games. Willis unsuccessfully attempted to trade Burden, but ending up placing him on waivers and releasing him following the season.
On July 3, 1980, Burden and three other men allegedly robbed a bank in Hempstead, Long Island. Burden was convicted after the three other men struck deals and testified against him, and was given a sentence of six to eighteen years. After serving two years, Burden's conviction was overturned when a court ruled that detectives did not possess search or arrest warrants when they raided Burden's home. Burden would later plead guilty to receiving stolen money in conjunction with the robbery, but was released after being given credit for time served.