Eric Bellquist, 41, was arrested on Thursday on suspicion of causing grievous bodily harm, following the incident on London's Putney Bridge.
He was later released without charge while inquiries continue, police said.
Mr Bellquist, a private equity firm partner, says he has "irrefutable proof" he was in the US at the time.
A statement released by lawyers acting on behalf of Mr Bellquist, who was detained at a residential address in Chelsea, said: "Our client has been wrongly implicated in this matter.
"He categorically denies being the individual concerned and has irrefutable proof that he was in the United States at the time of the incident.
"Consequently, we expect a swift resolution to this wholly untrue allegation."
Mr Bellquist works for Hutton Collins Partners and sits on the boards of the Wagamama and Byron restaurant chains, which are both owned by the firm.
On Monday, CCTV footage was released showing the woman, 33, narrowly avoiding serious injury when she was pushed into the path of an oncoming bus by a jogger on Putney Bridge.
The footage, captured on the morning of 5 May, shows a bus swerving to avoid the woman's head.
Afterwards the driver stopped the bus, at which point several passengers got off and went to help the victim.
About 15 minutes later the jogger came back the other way across the bridge.
The woman, who received minor injuries, tried to speak to him but he did not acknowledge her and carried on jogging.
The Met Police said it had received a "huge response" to its appeal for information.
Scotland Yard said the man officers arrested was still the subject of investigation but had not been released on official police bail.