Alfredsson was born in Gothenburg, Sweden. She represented Sweden in European Junior and Senior Team championships. She was a member of the Swedish team in the Espirito Santo Trophy World Amateur Team Championship in 1986 and 1988 and is a six-time Swedish national champion winning from 1981-1984, in 1986 and 1998.
She attended United States International University and graduated in 1988 with a degree in International Business and then tried a career in Paris as a model whilst flying with the Blue Angels and learning to ride a motorcycle. During 1986-1988 she played five times on the Swedish Telia Tour, winning at least once a year. She turned professional on 1 January 1989.
Alfredsson began her professional career on the Ladies European Tour where she was rookie of the year in 1989. The next year, in 1990, she claimed her maiden professional win at the Women's British Open. She won twice on the LET in 1991 and won once each on the ALPG and Japanese tours. She earned exempt status for the 1992 LPGA Tour season by tying for 17th at the LPGA Final Qualifying Tournament.
She earned Rookie of the Year honors on the LPGA Tour in 1992 and has won seven LPGA Tour events, including one LPGA major: the 1993 Nabisco Dinah Shore.
Alfredsson has continued to play a limited number of events in Europe, where she has won eleven events. She finished at the top of the European money list in 1998. She has been a member of the European team in the Solheim Cup five times: in 1990, 1992, 1994, 1996, 1998, 2000 and 2002. She was captain of the European Solheim Cup team in the 2007 Solheim Cup, in which Europe lost to the USA 12-16.
Alfredsson is married to former National Hockey League player Kent Nilsson and stepmother of his son, hockey player Robert Nilsson.