Details of Tuesday's arrest remain sketchy, but police confirmed operatives from its Force Intelligence Department and Intelligence Response Team were involved.
The suspect is expected to be taken to the police headquarters in Abuja for further questioning.
The police launched a manhunt for Adeyemi after the allegations about the PFIPC surfaced last week.
Tinubu's office said an official-looking letter creating the agency was fake.
Police forensic analysis had confirmed the signature of the president's chief of staff, Femi Gbajabiamila, on the disputed appointment letter had been forged, the presidency said.
The scandal has prompted calls for an independent inquiry from civil society groups, opposition politicians and senior lawyers.
Adeyemi has maintained his innocence in interviews with local media.
"My life is in danger," he said, according to local reports, though he promised to appear in court to clear his name.
But he was absent at the hearing on Tuesday. His lawyer, Genesis Francis, told the court he had been unable to persuade his client to attend, citing Adeyemi's safety fears.
The lawyer said the defendant had written an open letter to President Tinubu expressing those concerns.
Adeyemi had previously alleged the PFIPC was established in 2024 to attract foreign investment to Nigeria. However, there is no record of any deals being concluded.
BBC News Pidgin found the agency had secured office space within the Federal Secretariat, the sprawling government complex housing many ministries in Abuja.
It had also opened accounts with the Central Bank of Nigeria and appeared in the 2026 Appropriation Act with an allocation of 1.3bn naira ($950,000; £700,000).
However, the Accountant-General's Office said the PFIPC had never operated an account with the central bank, nor received any public funds or salaries.
According to court documents, Adeyemi and two others are accused of using forged official documents to establish and operate the council, opening multiple bank accounts in its name and seeking official recognition for the non-existent agency.
