The proposed legislation calls for new or increased taxes on a wide range of items including fuel and food as well as beauty products, crypto currencies and social media influencers.
Police fired several volleys of tear gas and arrested 11 people, bundling them into a police truck, to try to disperse the demonstration, AFP journalists at the scene said.
"Down down finance bill," chanted protesters as a group of about 100 marched towards parliament, which resumed on Tuesday after a recess and is expected to debate the legislation this week.
The demonstrations – which the organisers said had been notified to the police – have been dubbed "sita sita" (six six) as they were held on the sixth day of the sixth month.
Marchers waved placards reading "Will more taxation lead to low cost of living" and "Poverty is man-made".
"We are witnessing some chaos which is not right. We are being chased but we are fighting for our rights," said one of the protesters, Rodgers Obogi, a 23-year-old unemployed man. "We are demonstrating to express our frustrations, people need money, that money is being taxed twice."
President William Ruto is seeking to fill the government's depleted coffers and repair a heavily-indebted economy inherited from his predecessor Uhuru Kenyatta, who splurged on major infrastructure projects.
His government has drawn up a 3.6-trillion shilling ($26.2-billion) budget for 2023-2024 with the proposed new taxes expected to generate 289 billion shillings. According to Ruto, the bill will stimulate the country's economy, help combat unemployment and boost citizens' incomes, addressing problems that face ordinary Kenyans.
Critics accuse Ruto of rowing back on promises made during the August 2022 election campaign, when he declared himself the champion of impoverished Kenyans and pledged to improve their economic fortunes.
Opposition leader Raila Odinga's Azimio party has denounced the bill, saying Ruto's government wanted to "take billions from the pockets of some of the poorest people in this country while expecting them to cheer".
"We have refused to sit back and watch as Kenyans are being harassed to fix cash crunch caused by economic mismanagement, wasteful spending, corruption and skewed and incompetent hiring into critical public positions," Azimio said in a statement on May 30.
Odinga earlier this year led a series of protests over Kenya's cost-of-living crisis and his complaint that victory was stolen from him in the presidential election.