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Olsson, who lost to Reid in the final of last year's inaugural event, proved too strong for the Briton, prevailing 6-2 6-3 to reach the semi-finals.
The Scot, who won singles gold at the Rio Paralympics, will compete in the doubles with England's Alfie Hewett.
Hewett beat France's Nicolas Peifer 4-6 6-2 6-2 in his singles opener.
The 19-year-old will play Argentina's Gustavo Fernandez, who he beat to win his first Grand Slam title at the French Open last month, in the semi-final.
However fellow Britons Lucy Shuker and Jordanne Whiley were beaten by Japanese second seed Yui Kamiji and Dutchwomen Diede De Groot respectively in the women's draw.
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The wheelchair finals could be played on the 2,000-capacity court three this year.
Last year's were played on the far smaller court 17.
Gordon Reid's defence of his Wimbledon wheelchair singles title ended in the first round as he lost to Sweden's Stefan Olsson.