The two animals ran off while being taken up to summer pastures in Vorderthal in the canton of Schwyz on Tuesday
A farmer was eventually able to drive a suckler cow back to its stall. But as he was closing the gate, the animal broke loose and lightly injured him.
Another woman who had been trying to round up the two animals was then thrown against a parked car by the suckler cow and received more serious injuries, cantonal police said in a statement.
The woman was transferred to a specialist clinic by the Swiss air rescue service Rega, while the man was hospitalised.
The suckler cow was eventually returned to its stall but the other cow could not be caught and was eventually put down.
Hikers often encounter cattle on paths throughout the Swiss Alps. Attacks are rare but do occur, especially when the herd contains calves.
A German tourist from Berlin was killed in 2015 after walking through a field containing cows and their calves in the popular tourist area of Laax in the canton of Graubünden in south-eastern Switzerland.
In 2014, a family of tourists were attacked by a cow with a calf above Davos, also in Graubünden and in 2012 a woman was attacked by cows in a pasture above Saint-Gingolph in the canton of Valais.
Read also: How to protect yourself against cow attacks