Parliament agreed to the pay rise earlier this week in a session that was not televised.
Last month President John Dramani Mahama authorised an increase in MPs’ pay.
The BBC’s Sammy Darko in Ghana says both rises will be backdated to 2009 – which has caused a public outcry.
Our reporter says news of the pay increase, agreed by MPs for the executive, was slow to emerge because it took place in a closed-door session on Tuesday night.
This has angered Ghana Integrity Initiative which says such decisions should be debated in public.
“We have the right to know because we are tax payers,” Vitus Azeem, the head of the anti-corruption group, told Ghana’s Citifm radio station.
“If we know what has gone in to arrive at those figures, then we will also be able to make constructive comments on them. But if they hide it from us then that’s a problem.”
The president’s monthly salary has gone up from about $4,240 (£2,640) to $6,357, which is tax free.
The new salary for ministers, who also have benefits such as the use of two cars, a house with staff and an entertainment allowance, will be $4,770.
MPs’ salaries have been increased by $2,225 to $3,800 a month.
Our reporter says that while Ghana’s executive and MPs earn considerably less than some other African parliamentarians – like those in Kenya who earn nearly $10,000 a month – in comparison to other public officials in Ghana their salary is very high.
He says the monthly minimum wage in Ghana is about $75 and civil servants, such as teachers, earn below $500.
Mr Mahama is the interim head of state following the death of President John Atta Mills in July 2012.
Presidential elections will take place in the West African country in December.