Speaking on state TV, he also described the outbreak as "not something extraordinary."
Iran has had the highest number of deaths from coronavirus outside China, where it originated, and several officials have been infected -- including the head of Iran's emergency medical services, ILNA news agency reported on Tuesday.
The death of one top official was reported on Monday.
Khamenei said government bodies and the armed forces should give full support to the health ministry and that Iranian authorities have dealt transparently with the virus's spread.
"Don't violate the recommendations and instructions of the responsible authorities in terms of prevention, in terms of keeping hands, face and living environment clean and not infecting these and preventing the infection of these," he said.
Khamenei also said the outbreak should not be overblown.
"The issue is an issue that will pass. It's not something extraordinary," he said. "I don't want to minimize the issue but let's not make it very big either.
"It's an issue that has occurred, it's for a period ... that inshallah will not be very long."
Separately, Deputy Health Minister Alireza Raisi said 2,336 cases of coronavirus have been confirmed in Iran.
"Based on the latest statistics that have been compiled there have been an additional 835 definite new infections. Unfortunately we have 11 new deaths," he told state TV.
"With these numbers the definite number of new infections is 2,336 and the definite number of deaths has reached 77."
Those infected with coronavirus include head of emergency medical services, Pirhossein Kolivand, ILNA reported.
Lawmaker Abdolreza Mesri said 23 members of parliament have been infected, according to state TV-affiliated website YJC. He did not specify when they had been infected.
"Meetings between people and the representatives have been temporarily stopped," Mesri was quoted as saying.The announcement in a short period of time of dozens of deaths and hundreds of infections from coronavirus has led some Iranians on social media to accuse authorities of a cover