Jabeur, a rocket in the rankings after being tenth at the turn of the year, however, injured her knee when she played doubles with Serena Williams in Eastbourne earlier this week and is fighting against the clock to get well.
The other Swedish players got affordable draws against opponents who are about the same class as themselves.
95-ranked Rebecca Peterson is set against the Slovak Anna Schmiedlova, ranked 84th
Peterson has had a difficult period behind him and did not even start in the latest Grand Slam tournament French Open due to a sprained foot.
Sweden's best men's player Mikael Ymer (ranked 88th) will face the German Daniel Altmaier (64) in a meeting between two 98s born just three days apart in September.
Serena against low ranked French
The former world setter Serena Wiliams (dropped in the ranking to place 1204) who did not play single in a year, when she injured her knee in Wimbledon's first round, will face Frenchwoman Harmony Tan (113) in the first round.
The 40-year-old American received a wildcard from the organizer.
This year's tournament is played without ranking points, a penalty awarded by the WTA and ATP because Wimbledon ported Russian and Belarusian players.
This means that world setter Daniil Medvedev will not start.
World runner-up Alexander Zverev is also missing after the serious ligament injury in the French Open.
However, second-seeded Rafael Nadal will start after his win in the French Open.
The Spaniard is up against the Argentine Francisco Cerundolo (ranked 42nd).