The 68-bed home in Stubbington Lane was approved by councillors who reluctantly imposed the car ban condition set by Natural England.
It comes as Natural England has drawn up a plan to prevent disturbance to the New Forest. This includes recommending planning conditions on developments in council areas within a 13km radius of protected sites.
As well as Fareham, the zone includes Eastleigh, New Forest, Southampton, Test Valley and Wiltshire council areas.
Speaking at a recent planning meeting, Warsash councillor Michael Ford said the condition was utterly bizarre.
He said: ‘My first thought when I read this was: has this come out of the Soviet Union or the People's Republic of China?
'You will have no children - you will have no cars,’ he said.
He said he fears the same condition could be applied in further planning applications yet to come.
It comes after ecologists were commissioned to research areas that negatively impact certain sites in the New Forest previously given special protection by the European Union.
The Zone of Influence report, by Footprint Ecology, draws up a 13.8km radius catchment area in which it's thought new developments could have an adverse effect.
Footprint Ecology recommended excluding Fareham in the 13.8km implementation area - due to the Solent acting as a barrier - but Natural England included the borough anyway.
A spokesperson from Natural England said: ‘Most visitors to New Forest designated sites originate from within a 13.8km radius of the protected site boundaries.
‘It is Natural England’s advice that new residential development within this zone is likely to have a significant effect on the sites via recreational impacts, alone or in combination with other plans or projects, without suitable mitigation.
‘Most of the borough of Fareham lies within the 13.8km buffer zone and telephone survey data indicates that frequency of visits is similar to those in the neighbouring borough of Eastleigh.’
Next week Fareham Borough Council will consider an interim mitigation solution.
This will include ‘alternative recreational opportunities’ such as parks and open spaces to deflect visits away from the New Forest.
If the solution is not approved, Natural England has the power to thwart planning applications that could have adverse effects on the New Forest.
There are concerns this could create a backlog of planning permissions that could make the council fall short on its housing targets set by the government.
Cllr Simon Martin, executive member for planning, said Natural England used 117 telephone surveys to determine that Fareham residents make 15 visits to the New Forest each year.
‘I don’t think that’s particularly significant,’ he said.
‘Natural England at the moment are putting objections in and saying things shouldn’t happen until this issue of the New Forest disturbance has been sorted out.
‘We could be in a position where other park areas like the South Downs come up with something similar - there has to be a common-sense solution.
‘I do detect from having spoken with various people in government that this is a more contentious issue and effectively it’s an unfair way of making sure that areas in the New Forest are properly looked after.’
Suella Braverman, MP for Fareham, also shares concerns about the scheme - and the cost for developers of any mitigation measures.
‘I was recently made aware of reports that under the mitigation plans, developers in Fareham will now have a premium of £156 per planning application,' she said,
‘I have now been informed that in practice this has gone up to £247 per unit, in one case.
‘This is unacceptable, considering that the New Forest ‘Zone of Influence Report’ excluded Fareham from the 13.8km implementation area, which has now been reversed and the 13.8km zone has been applied to Fareham.
‘I am now seeking urgent discussions with Natural England to interrogate these measures and to closer examine their modelling, which I believe is misinformed and unrepresentative.’
Councillors approved the demolition of buildings at Hammond Industrial Estate to make way for the new care home in Fareham.
The application was brought by Frontier Estates Ltd.