Hundreds of protesters poured into the Kenyan capital, as well as the coastal city of Mombasa and the lakeside city of Kisumu, where the opposition enjoys strong support, but were dispersed by police who fired tear gas canisters at them.
Protesters lit bonfires and erected barricades on some major highways.
Enforcement of the newly signed law increasing taxes has been suspended by a court pending the hearing of a case brought by an opposition senator challenging its legality.
However, the government has applied the tax on petroleum products.
Nairobi Police Commander Adamson Bungei told The Associated Press on Friday that “more than 20 people had been arrested by midday” but did not reveal what charges they will face.
The opposition had called the demonstrations to protest new taxes on petroleum products, salaried workers and companies.
Opposition supporters are expected to gather at a rally in Nairobi, where Odinga said he would announce new measures to fight the new taxes.
Police said the planned rally was legal, but the ongoing demonstrations were illegal.
On Friday, some shops in the main cities remained closed.