The Consular Affairs Department closed its headquarters on Chaeng Watthana Road after protesters started gathering there on Monday.
Those who apply for a passport at the moment can only receive the document by mail, Foreign Ministry spokesman Sek Wannametee said.
Mr Sek said the department can only take up to 2,500 new passport requests a day from its Bang Na and Pin Klao branches.
All other branches in other provinces have also been closed temporarily since Monday due to the protest.
A source said the Consular Affairs Department's Chaeng Watthana office can produce about 8,000 passport books a day under normal circumstances.
The number of people applying for passports at the Bang Na and Pin Klao branches has doubled from 800 people a day normally.
Numbers of those using other services, such as translating and notarising documents, have increased to more than 100 people per day.
The Bang Na branch is opening half an hour earlier than usual at 8am, but both branches close at 3pm.