The five-time Grand Slam winner, 28, revealed on Monday that she tested positive for meldonium in January.
‘Clearly if you are taking performance-enhancing drugs and you fail a drugs test, you have to get suspended,” said Briton Murray, the world number two.
Russian Sharapova will be provisionally suspended from 12 March.
The former world number one says she has been taking the drug, which was added to he World Anti-Doping Agency’s banned list on 1 January, for health reasons for the past 10 years.
Sharapova is one of several athletes to have tested positive for the heart drug, including 1500m world champion Abeba Aregawi, 2015 Tokyo Marathon winner Endeshaw Negesse and Russian ice dancer Ekaterina Bobrova.
‘I think, since 1 January, there have been 55 different athletes who have failed tests for meldonium, ‘Murray told BBC Radio 5 live.
‘I find it strange that there’s a prescription drug used for heart conditions and so many athletes competing at the top level of their sport would have that condition.
That sounds a bit off to me.’
Murray also said tennis needed to do more to combat the threat of doping.
‘It’s better than it was a few years ago,” he said. ‘Last year I certainly got tested a lot, but this year I have been tested twice, three months into the year, which clearly is not enough.’
Women’s world number one Serena Williams said Sharapova’s positive test was not indicative of a wider drug problem within tennis.
‘We live in a massive world with billions of people and we have a few people that do things and it makes people scared, but that doesn’t make the whole world a bad place,” she said.
‘That’s the same thing with tennis.
‘The majority of the players really pride themselves on having integrity and playing with that.’
Williams, who said she was ‘terrified’ of taking any supplements, has offered her support to Sharapova, saying she had shown “a lot of courage”.