The world No 1 had followed up her Wimbledon triumph on Saturday by notching a 40th victory of the year with a 6-2 6-1 demolition of Belgium’s Ysaline Bonaventure in her first-round match in Bastad on Wednesday.??
However, the top seed failed to make her second-round encounter with Klara Koukalova of the Czech Republic on Thursday after being troubled by an issue with her elbow.
The American won the Swedish claycourt event in 2013 but will have to wait at least another year to follow that up.
Williams remains scheduled to appear at the hardcourt tournaments in??Stanford, Toronto and Cincinnati before aiming for a fifth straight Grand Slam at the US Open.
The only other first-round match saw seventh seed and home hope Johanna Larsson beat Richel Hogenkamp 6-1 6-3.
The first three second-round matches also took place on Wednesday and there was a big surprise as Spanish WTA Rising Star Lara Arruabarrena rallied from 4-2 down to take a lengthy 57-minute first set and then totally outplayed second seed Samantha Stosur for a 7-6 (7-5) 6-0 win.
Jana Cepelova and Mona Barthel joined Arruabarrena in the quarter-finals after successes.