The party said it admired the former Tory MP for quitting over Heathrow expansion and praised his commitment to the Brexit campaign.
Mr Goldsmith quit in protest at the government's backing for a third Heathrow runway and will contest the by-election as an independent.
The poll takes place on 1 December.
The Conservatives are not fielding a candidate against their former MP, while the Liberal Democrats have vowed to make the by-election about Brexit - which Mr Goldsmith backed - not Heathrow.
A UKIP spokesman said: "Zac Goldsmith has resigned on a matter of principle and UKIP admire him for having the courage to do so. UKIP have always believed that Gatwick was a preferred option to Heathrow."
It said party leader Nigel Farage and the ruling executive committee thought Mr Goldsmith was a "principled man, who was fully committed to helping get Britain out of the European Union" and so had decided not to put forward a candidate to challenge him.
The spokesman said the Lib Dems were committed to overturning the EU referendum result, adding: "UKIP are encouraging all of our supporters and voters to support Zac Goldsmith in his bid to become an independent MP."
Mr Goldsmith had a 23,015 majority at the 2015 general election, with the Lib Dems finishing second.
Government Chief Whip Gavin Williamson formally triggered the contest by moving the writ at the start of business in the Commons on Thursday.
UKIP says it will be backing Zac Goldsmith in the Richmond Park by-election and will not be fielding a candidate against him.