The Independent Police Complaints Commission (IPCC) is investigating the death of Ian Tomlinson on 1 April in the City of London.
The criminal inquiry began after video footage emerged of Mr Tomlinson apparently being shoved by a policeman.
The officer pictured in the footage has been suspended after coming forward.
IPCC chairman Nick Hardwick said: "This is now a criminal investigation for which someone may face very serious charges.
"The decision we took meant that we are now in the best possible position to bring that prosecution successfully if we need to do that.
"We will be independent, we will be fast and we will be effective."
The IPCC has yet to interview the officer involved but said it intends to "as soon as possible".
Additional footage broadcast by Channel 4 News appeared to show an officer hitting Mr Tomlinson with a baton.
IPCC chairman Nick Hardwick has rejected suggestions that the police were not co-operating with the investigation.
He said: "The police, both forces, have given us the information that they have available when we asked them for that. It's not true that they haven't co-operated with us."
An earlier statement from the IPCC said: "The IPCC called for the officer to be suspended. The MPS has now informed us that the officer has been suspended with immediate effect."
A Metropolitan Police spokesman said: "In order to maintain public trust in the police handling of public order events, a Metropolitan Police territorial support group police constable has been suspended, effective immediately, in relation to the IPCC investigation into the death of Ian Tomlinson.
The IPCC began an independent criminal probe on Wednesday after the first video footage of Mr Tomlinson apparently being shoved to the ground emerged.
It has ordered a second post-mortem examination as part of the inquiry.
On Thursday the Met acknowledged Mr Tomlinson came "into contact with police" before he died.
Initially the force said it was unaware he had sustained the alleged assault and said its officers' first contact with him was when they gave him medical aid before he died.
But it denied trying to "cover up" the incident.
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