The house of representatives on Wednesday voted 97 to 82 in favour of making the checkups mandatory starting at the age of 75.
The proposal was promoted by Maximilian Reimann, a Swiss People's Party politician from the canton of Aargau, who is 73, the ATS news agency reported.
It calls for the government to conduct an awareness campaign so that elderly drivers can decide for themselves when they should stop driving.
Swiss regulations concerning elderly drivers are significantly stricter than in neighbouring European countries.
In France, Austria and Germany seniors who drive are not subject to regular checkups and they can decide when they want to relinquish their driving permits.
Switzerland doesn't need to go that far but it's time to end discrimination against the elderly in the country, Reimann said, according to ATS.
The number of retired foreigners who are driving on Swiss roads has not led to a higher rate of accidents than among their counterparts living in Switzerland, he argued.
Left-wing parties, however, maintained that medical checks for those 70 and over were not discriminatory and started at a good time.
It cannot be contested that driving aptitude diminishes with age, even is this is variable depending on the individual involved, Roger Nordmann, a Socialist from the canton of Vaud said.
The initiative goes now to the senate (upper house of parliament) for consideration.