The order will apply to the federal and local Delhi governments.
India's Supreme Court will hear a plea against private ownership of diesel vehicles on 15 December.
Delhi is experiencing hazardous levels of pollution due to diesel emissions, construction dirt and the burning of crop stubble in farms around the city.
Air pollution causes more than 600,000 premature deaths in India each year.
The tribunal order will not apply to private owners of diesel cars, Delhi government lawyer NP Singh told the BBC.
However, the country's top court is due to hear a petition asking for the banning of privately-owned diesel vehicles next week.
In recent days, pollution levels in Delhi have reached alarming levels and last week, the Delhi high court said the city resembled a "gas chamber".
The Delhi government then announced that from 1 January 2016, private vehicles with odd and even registration numbers would only be allowed to operate on alternate days.
The transport department would run extra buses, a government official said.
New car sales are soaring in India, with 1,400 extra cars taking to the capital's streets every day.
Earlier this month, India said it would require vehicles to abide by stricter emissions standards by 2019, three years ahead of a previous deadline.
Last month on the night of Diwali, the Hindu festival of lights, air pollution in Delhi reached 40 times the limit recommended by the World Health Organisation (WHO).
The capital city is not alone - India has 13 of the world's 20 most polluted cities, the WHO reported last year.
India's National Green Tribunal has told the government not to buy any more diesel vehicles amid worsening pollution in the capital, Delhi.