Basilashvili, from Georgia, is the 24th seed and represents a tough test for Murray.
The Scot is making his first appearance in the men’s single at the Championships since 2017 following a hip resurfacing operation.
The 34-year-old had to rely on a wild card to get into Wimbledon, with his ranking having dropped outside the top 100.
British wild card Jack Draper will make his Wimbledon debut against top seed and defending champion Novak Djokovic.
Draper, 19, showed his considerable promise by reaching the quarter-finals at Queen’s Club last week and now faces the toughest test in tennis against the man going for a third consecutive grand slam title.
British number one Dan Evans, who is seeded 22nd, faces a potentially difficult opener against experienced grass-court campaigner Feliciano Lopez.
Sixth seed Roger Federer, who has been drawn in the opposite half to Djokovic, opens against another experienced grass-court campaigner in France’s Adrian Mannarino.
British number two Cameron Norrie, seeded for the first time at a grand slam after his stunning start to 2021, takes on Frenchman Lucas Pouille.
Second seed Daniil Medvedev begins his campaign against German Jan-Lennard Struff.