"It's not up to me to decide the punishment, but if you're taking performance enhancing drugs and you fail a drugs test, you have to get suspended," Murray told reporters at the Indian Wells tournament in Palm Springs on Thursday.
"If you're taking a prescription drug and you're not using it for what that drug was meant for, then you don't need it, so you're just using it for the performance enhancing benefits that drug is giving you. And I don't think that that's right."
The drug, produced in Latvia but unavailable for purchase in the United States where Sharapova is based, was only added to the World Anti-Doping Agency (WADA) list of banned substances in January, shortly before her positive test at the Australian Open.
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Manufactured for people suffering from heart problems, it can also increase blood flow and improve exercise capacity.
Sharapova, who will be provisionally suspended by the International Tennis Federation from this weekend and faces up to a four-year ban, told a news conference in Los Angeles on Monday that she had been taking the drug for 10 years.
She said she was first given it by a family doctor after she frequently became sick, had irregular electrocardiogram results, a magnesium deficiency and a family history of diabetes.
"I read that 55 athletes have failed tests for that substance since January 1," said Murray.
"You just don't expect high-level athletes at the top of many different sports to have heart conditions."
The highest-paid woman in sports, Sharapova has already lost support from some sponsors, with Swiss watchmaker TAG Heuer cutting ties this week, while Nike and Porsche have distanced themselves from her.
Murray said Head's announcement that it had extended its contract with the five-times grand slam champion was "a strange stance" given the events of the last few days.
"I don't really know what else to say on that, but that's not something I believe," he added.
"I think at this stage it's important really to get hold of the facts and let things play out, like more information coming out before making a decision to extend the contract like that, in my view. I personally wouldn't have responded like that."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Ian Ransom)
