Kabund's lawyer Henriette Bongwalanga said he was arrested on Tuesday after a hearing at the attorney general's office.
A police source said Kabund had been taken to Makala Central Prison in Congo's capital Kinshasa.
"They did not respect the procedure. Today they came after the hearing and (arrested) him despite his (parliamentary) immunity," his attorney said.
His lawyers say he is accused of contempt of the head of state after a speech calling him "a danger."
The former vice president of parliament and current lawmaker had a falling out with President Felix Tshisekedi earlier this year, after which he launched his own political party.
He has been under investigation in recent weeks on charges that authorities have not specified.
Kabund was a leading figure behind Tshisekedi's rise to power and their fallout has highlighted emerging fault-lines in the country's leadership. This could spell uncertainty for the future of the ruling Sacred Union coalition as the 2023 presidential election nears, political analysts have said
The justice ministry could not be reached for comment and a spokesperson for the government declined to comment.