He moved on to Premier Division team Celtic in December 1995. At Celtic, injuries partly ruined his first two seasons. In the 1997–98 season, Wieghorst played 31 of 36 league matches for Celtic, as the club won its 36th Scottish championship to end "Old Firm" archrivals Rangers' nine-year strangle-hold of the title. In 2000, Wieghorst was diagnosed with the Guillain–Barré syndrome, and following treatment he spent a year in recovery before returning to play in a November 2001 Scottish Cup game. He played three league games for Celtic late in the 2001–02 season, before he returned to Denmark.