Blocked from selling Yemen’s oil, the Houthi-led government has slipped into a financial crisis after four months of conflict with a Saudi-led military coalition.

The Houthis wrested control of government in the capital San’a in February and sent Western-backed President Abed Rabbo Mansour Hadi into exile the following month. They have since held the levers of power, having taken over government ministries and the central bank.

Oil...