World number 49 Medvedev, making his Wimbledon debut, goes on to face Belgian qualifier Ruben Bemelmans for a place in the last 32.
It was Wawrinka's sixth first round loss at the All England Club, although his efforts were hampered by a left knee injury which required an ice pack at the changeovers.
It also meant that 33-year-old Wawrinka's hopes of becoming just the sixth man to complete the career Grand Slam were ended for another year.
Having lost in the first round at Queen's Club last month, Wawrinka's grass-court campaign amounted to two matches and two defeats.
For 21-year-old Medvedev, it was a first win at the Grand Slam level, coming on the back of an impressive grass court season.
He made the semifinals in Eastbourne last week where it took Novak Djokovic to stop him, as well as the quarterfinals at 's-Hertogenbosch and Queen's.
"A year ago I was ranked 250. If someone told me in one year I would win on Centre Court I would tell you you are joking," said Medvedev, who kissed the grass of Centre Court to celebrate his victory.