Asher-Smith, who won her world title in the same city in 2019, ran a strong bend but faded down the home straight as Olympic bronze medallist Gabrielle Thomas of America took the win ahead of Jamaica’s Shericka Jackson.
In windy conditions which had forced the men’s pole vault to be postponed, Asher-Smith clocked 22.37 seconds, with Thomas equalling the meeting record with a time of 21.98secs.
It was the 26-year-old Briton’s first top-level race of 2022 following low-key appearances over 300m and 400m at Lee Valley in April and came ahead of next weekend’s showdown against Olympic champion Elaine Thompson-Herah over 100m in Birmingham.
Asher-Smith claimed her second relay Olympic bronze medal at last summer’s Tokyo Games after failing to reach the 100m final and pulling out of the 200m following a hamstring problem.
Her British team-mate Beth Dobbin finished sixth in Doha in 23.06s, with Dan Rowden earlier fourth in the men’s 800m in 1:49.56 in a race won by Kenyan teenager Noah Kibet.