First Republic Bank’s stock fell 20% in after-hours trading on Monday despite stronger-than-expected first-quarter profit from the bank, as deposits disappeared amid concerns about regional banks.

San Francisco-based lender First Republic FRCsaid that deposits fell 41% in the quarter, though withdrawals have stabilized in April. Executives plan to reduce the bank’s workforce by 20% to 25% in the current quarter. Based on the bank’s 7,213 full-time employees as of Dec. 31, as disclosed in its annual report, the layoffs could...