In a case of unfortunate timing during tax-filing season, the Internal Revenue Service’s headquarters in Washington will remain closed for the remainder of the week, after a Monday-afternoon fire in the building’s basement.

The building has been closed since people were evacuated Monday afternoon. More than 2,000 people, including the tax agency’s senior executives, work in the 80-year-old building on Constitution Avenue. The IRS headquarters lies between the new hotel being built by Republican presidential candidate Donald...