Born in Aarhus and a youth product of Viby IF, Povlsen also played in The Netherlands, Spain and Germany, until a knee injury forced him to retire, at only 28 years of age.

Before the injury, Povlsen rose to prominence at FC Cologne, before settling at Borussia Dortmund, with whom he won the 1995 Bundesliga and played the final half of his career.

He moved abroad in 1986, when he signed for Spanish club Castilla CF, the reserve team of multiple European champions Real Madrid.

Even though he wasn't a top goal scoring striker, Povlsen's speed and work rate endeared him to the fans, and he won two sets of silver medals, as the Köln team finished second in the 1988–89 and 1989–90 Bundesliga seasons.

Although he had a short appearance in March 1995 against Eintracht Frankfurt, and thus was a part of the 1994–95 Bundesliga winning Dortmund side, Povlsen ended his playing career due to his knee injuries.

The forward played all five Denmark matches in the tournament, and scored once: In the semi-final penalty shootout against the Netherlands, Povlsen pinned a goal after an intense battle of nerves with Dutch keeper Hans van Breukelen, his former PSV teammate.