WASHINGTON—Sen. Kamala Harris raised $1.5 million from 38,000 donors online in the 24 hours after announcing her presidential run Monday morning, her campaign said.

The California Democrat saw a burst of $1 million in contributions in the first 12 hours after her appearance on ABC’s “Good Morning America” and the simultaneous release of an online video, her campaign said, adding that the average donation was about $37.

Those initial donation numbers are competitive with Vermont Sen. Bernie Sanders’s 2016 presidential campaign kickoff. His team said at the time that he raised $1.5 million from 35,000 donors in the first 24 hours after his April 30, 2015, announcement. Mr. Sanders, who ultimately raised 85% of his $238 million in increments of $200 or less, is weighing another presidential run.

Democrats have put a premium on grass-roots fundraising ahead of the 2020 campaign, with the Democratic National Committee planning to include some kind of small-money metric in its debate qualifications. The rules haven’t yet been set.

The Democratic field is expected to grow to as many as two dozen candidates, with several, including New York Sen. Kirsten Gillibrand and Massachusetts Sen. Elizabeth Warren, already announcing exploratory committees. A crowded primary could make fundraising a challenge.