Britain’s world No 3 needed just 74 minutes to complete a 6-2 6-2 victory over the Russian-born German, who is ranked 650 places below the top seed.
Having dominated the first set, Murray had more problems dealing with 27-year-old left-hander Zverev in the second, but still defended all six break points he faced for a comfortable success as he starts his build-up to the French Open.
“It wasn’t too easy, he had a different style to most other players and it was tricky playing against a left-hander, but I got the important points,” said the Scotsman, who is also playing doubles in Munich.
“He was returning from a long way back.
“My forehand went better than my backhand, but it was a good first match for me.”
This was Murray’s first singles match since marrying Kim Sears earlier this month.
He has already made the most of his time in Bavaria by watching Bayern Munich’s German Cup semi-final defeat to Borussia Dortmund live on Tuesday.
Murray faces a tougher test in Friday’s quarter-finals when he plays Lukas Rosol after the Czech, ranked 41st in the world, booked his last-eight berth with a 7-5 6-2 win over Ukraine’s Sergiy Stakhovsky in their second-round match.??