Foreign migrants will have to live in Britain for a year before they can claim civil legal aid as part of reforms to save £300 million a year.
Justice Secretary Chris Grayling said some migrants were using the system to settle custody cases despite being in the country for "extraordinarily short periods of time".
He said the measures would be "difficult but sensible" and insisted the move was "not about denying people access to justice".
In an interview with The Sunday Telegraph he said: "There are a number of areas where somebody who comes to this country even on a tourist visa can access civil legal aid. We are going to change that.
"There have been examples of people who have come to the country for extraordinarily short periods of time who have had a relationship breakdown and then they end up in our courts at our expense to determine custody of the children.
"This will exclude people who enter the country illegally, who up to now have been able to access our legal aid system in a way I don't think should ever have happened."
Mr Grayling also said he wants to curb the criminal legal aid bill, telling the newspaper nobody whose earnings came from the public sector "should reasonably expect" to top the Prime Minister's £142,000 annual salary.
The package of measures being unveiled next week will stop prisoners using legal aid for cases that do not relate to the length of their sentences, according to the newspaper.
"I am proposing to take legal aid away from prisoners who don't like the prison they are in, or don't like the cell they are in, or don't like a part of the regime," Mr Grayling told The Sunday Telegraph.