A federal judge in New York ruled Wednesday that President Trump can’t block subpoenas that House Democrats sent to two banks asking for documents related to his business and family.

The ruling, which mirrored one by a federal judge in Washington, D.C., earlier this week, came as the result of a lawsuit filed late last month by Mr. Trump and his three adult children against Deutsche Bank AG and Capital One Financial Corp. Mr. Trump sought to block the banks from complying with the subpoenas for financial documents about his...