Rev. Canon Evans Omollo said he was outraged that anti-riot officers lobbed teargas canisters and fired live bullets in the church compound, harming several protesters.
Police officers are prohibited from making official comments on incidents, policies, or procedures without clearance.
The two officers have been suspended from the National Police Service, Inspector General of Police Japhet Koome said in a press release.
The KMPDU and several groups want Koome to retract his directive to police commanders and apologise.
The Nairobi boss has also been slapped with a Sh500,000 fine for skipping the meeting.
The operation had recorded key successes but towards the end of last year, there was a resurgence of spontaneous attacks that have persisted in recent months.
The unit takes over the probe from Nairobi Regional Police Commander Adamson Bungei.
Interior Cabinet Secretary Kithure Kindiki revealed before a joint sitting of the National Assembly and Senate Committees on National Security, Defence, and Foreign Relations that the deployment of 1000 Kenyan police officers to a United Nations-backed peacekeeping mission in Haiti would amount to Sh36.5 billion.