President Lazarus Chakwera told MPs that the targeting of the government department amounted to a “serious national security breach”.
He revealed that the hackers were asking for a ransom.
But the president said the government would not give in to their demands and was working to resolve the problem.
“We are not in the business of appeasing criminals with public money, nor are we in the business of negotiating with those who attack our country,” he said on Wednesday.
Demand for passports is high in Malawi with many young people looking to migrate in search of job opportunities.
Mr Chakwera said he had given the immigration department three weeks within which it should provide a temporary solution and resume the issuing of passports, while waiting to regain control of the system.
He said a long-term solution with additional security safeguards would be developed.
For the past two weeks, Malawi has not been issuing passports for what officials said was “a technical glitch”.
Mr Chakwera only revealed for the first time on Wednesday that the immigration system had been “hacked” without mentioning who the hackers were suspected to be.
No other details have been given about the cyber-attack including the possible implications in terms of personal data security.
Malawians have been demanding answers over the persistent delays in the issuance of the travel document.
This is not the first time that there has been a suspension in recent years.
Last year, the government paused giving out new documents after running out of passport booklets, with an official saying that the problem was being worsened by a shortage of foreign currency.
There have been issues since 2021 when the attorney-general’s office terminated a passport contract with a company that had been offering the service, citing irregularities.
Some frustrated Malawians have in the past faulted the government over the continued backlog of applications amid allegations of corruption.
For now, anyone who does not have a passport or whose passport has expired cannot acquire a new one and therefore cannot travel.