"The recent outbreak of swine flu calls for national emergency funding to respond," Tsvangirai told a doctors conference in Harare.
"We don’t want a repeat of the cholera experience of last year," Tsvangirai said, but did not indicate how the cash-strapped government would find the additional money.
More than 2,400 people died of cholera over the last year, and UN officials have warned that the deadly but preventable disease is likely to erupt again.
The confirmation of the A(H1N1) virus has heightened fears about Zimbabwe’s health system, which has been decimated by a decade of economic free-fall.
Doctors at state hospitals have been on strike for the last week demanding better salaries and the restoration of US dollar allowances that were withdrawn last month by the government and aid agencies.
Tsvangirai urged doctors to return to work, saying the government was trying to address their concerns.
"I also urge those health professionals who have embarked on industrial action to recognise the efforts of the ministry of health and the Health Service Board," he said.
"I am confident that, as Zimbabwe gets back on its feet, we will all benefit."
Doctors receive a salary of US$170 US dollars, but are demanding a basic salary of up to US$3,000 and to be paid according to their level of experience.
Last month, the government increased salaries of civil servants from US$100 to US$150 US, while giving doctors US$170.