Though Prime Minister Antonio Costa has insisted the appointments were all based on merit, the revelations have brought accusations of nepotism and wide public criticism on social media.
Environment secretary Carlos Martins announced he was resigning because he didn't want the controversy over his cousin's appointment to damage the government.
Later, in the Republican Assembly, Portugal's parliament, the parliamentary leader of the main opposition Social Democratic Party, Fernando Negrao, said "the government has overstepped the mark" in handing jobs to family relations.
But Costa, the prime minister, told lawmakers that the issue had never been raised before and so the rules were unclear over what kinds of relationship should be permitted between government members and the people they appointed.
"It would be interesting to have a level-headed debate about it," Costa said. "It's just a pity it comes now, with elections on the horizon."