Malawi Justice Minister Ralph Kasambara suspended the laws Monday because he said he wanted a debate on whether to keep them, the human rights group said in a statement.
The action was "a historic step in the fight against discrimination in the country," said Noel Kututwa, AI's Southern Africa director.
"We urge the government not to lose momentum on this basic human rights issue and to ensure the full repeal of these discriminatory and hate-filled laws," he added.
Kututwa charged the anti-homosexuality laws violated Malawi's obligations under the Malawian constitution, the International Covenant on Civil and Political Rights and the African Charter on Human and Peoples' Rights.
In 2010, Malawi sentenced two men to 14 years in prison after they got married, CNN reported. They were pardoned after an international outcry.
Foreign donors have threatened to withhold aid from countries with anti-gay rights policies. In response, President Joyce Banda earlier this year said the laws would be reviewed.
Sodomy laws were introduced throughout Africa while the continent was under colonial rule.