“We [will] drop all the laws violating the human rights in Sudan,” Justice Minister Nasredeen Abdulbari said.
A raft of new laws were passed last week but this is the first public explanation of their contents.
Sudan has also banned female genital mutilation (FGM).
Under the new laws, women no longer need permission from a male relative to travel with their children.
The reforms come after long-time ruler Omar al-Bashir was ousted last year following massive street protests.
Non-Muslims are now allowed to consume alcohol in private, however the ban on Muslim drinking remains, Mr Abdulbari told state TV.
Non-Muslims could still be punished if they are caught drinking with Muslims, the Sudan Tribune reports him as saying.
He explained that the government was trying to safeguard the rights of the country’s non-Muslims, who constitute an estimated 3% of the population.
They are now allowed to drink, import and sell alcohol.
“We are keen to demolish any kind of discrimination that was enacted by the old regime and to move toward equality of citizenship and a democratic transformation,” he said.
The laws were initially approved in April but the BBC’s Mohamed Osman in Khartoum says they have only now taken effect.