Sharapova tested positive for the drug which the World Anti-Doping Agency (Wada) added to their list of banned substances on 1 January.
Head wants Wada to scientifically prove why the drug should be banned.
The company believes the drug should not be prohibited but instead come with a dosage limit.
Russia’s Sharapova tested positive at the Australian Open in January.
The five-time Grand Slam champion, 28, will be suspended from 12 March and could face a four-year ban.
She has already lost the backing of key sponsors, but Head, who plan to extend their contract with Sharapova, said she made an “honest mistake”.
Britain’s Andy Murray, who is also sponsored by Head, said the manufacturer had taken a “strange stance”.
A statement from Head said: “We question Wada’s decision to add meldonium to its banned substances list in the manner it did; we believe the correct action by Wada would have been to impose a dosage limitation only.
“In the circumstances we would encourage Wada to release scientific studies which validates their claim that meldonium should be a banned substance.”
Meldonium, also known as mildronate, was developed to treat diabetes and various heart-related diseases.
Sharapova has taken the drug since 2006, after frequent bouts of flu, abnormal electrocardiogram results and some indicators of diabetes.
Meldonium’s inventor Ivars Calvins told BBC Radio 5 live that athletes could die if they are denied access to the drug.