In the men's draw, Britain's Australian Open champion, Gordon Reid, has been drawn to face France's Nicolas Peifer.
Norfolk's Alfie Hewett faces Dutchman Joachim Gerard, with the matches scheduled to be played on Thursday.
The third British player in the ladies singles, Louise Hunt, will face Marjolein Buis of the Netherlands.
The ladies final will take place on 9 July, with the men's final the following day.
The total prize money for the wheelchair events at Wimbledon this year is £200,000, the highest on offer at any of the Grand Slam tournaments.
Wheelchair doubles has been played at the Championships since 2001, but this is the first year in which singles has been included.
Stephane Houdet (Fra) [1] v Maikel Scheffers (Ned)
Gustavo Fernandez (Arg) v Stefan Olsson (Swe)
Nicolas Peifer (Fra) v Gordon Reid (GB)
Alfie Hewett (GB) v Joachim Gerard (Bel) [2]
Jiske Griffioen (Ned) [1] v Sabine Ellerbrock (Ger)
Louise Hunt (GB) v Marjolein Buis (Ned)
Jordanne Whiley (GB) v Lucy Shuker (GB)
Aniek van Koot (Ned) v Yui Kamiji (Jpn) [2]
US Open champion Jordanne Whiley will face fellow-Brit Lucy Shuker in the quarter-finals of the first wheelchair singles competition at Wimbledon.