The move reflects concerns from local residents and businesses about air quality, Westminster City Council said.
A team of traffic marshals will patrol the borough and ask car idlers to switch off their engines, it said.
The London Taxi Drivers' Association (LTDA) said the move would not help abate London's air pollution problem.
The penalties will come into force on 1 May, as a "last resort".
The new policy follows Camden Council's fines for buses which idle for too long, introduced in 2011, and Islington Council's fines for idling vehicles introduced in August last year.
Westminster has the highest proportion of deaths attributable to air pollution, excluding the City of London, in the country, a report by the council said.
An air pollution monitoring station in Oxford Street, in the borough, recorded the acceptable limit set for air pollution - 200 micrograms per cubic metre - was broken 1,503 times in 2014.
A comparable station in Sutton did not break the limit at all last year.
Steve McNamara, general secretary of the LTDA said the fines were "absolute tosh" and a public relations and money raising exercise from the council.
He said: "It is not going to do anything constructive to tackle the pollution crisis in London. When was the last time you saw someone idling in the city? It doesn't happen.
"One of the real problems is cars stuck in traffic - research has shown pollution is up by 30% in areas of heavy traffic. Do something to help get the traffic moving."
Mr McNamara said another key factor was the number of diesel cars in the capital which emit greater levels of nitrogen oxides - which can cause health problems.
He said the move was "ironic" considering Chancellor George Osborne's incentives to diesel vehicles which were exacerbating the problem.
Neil Greig, director of policy and research at the Institute of Advanced Motorists, said the "key issue" would be how the marshals enforced the fines.
He said: "If they target private car drivers pulling up for a moment in relatively clean, modern cars in a draconian way - whilst ignoring old buses, coaches, large trucks, utility company vans or taxis idling for long periods - then it will quickly be seen as yet another revenue-raising exercise."
Motorists in Westminster who sit in a stationary car with the engine running and refuse to turn it off are to be fined £20.