Sir Mark was "very concerned" by the number of victims coming forward
The government says it wants an "urgent" meeting with a top judge over fears changes to the law have stopped victims reporting domestic violence.
Sir Mark Potter, President of the Family Division, has said the Domestic Violence Act's impact concerned him.
Another judge told the Times that since the 2007 law was introduced, up to 25% fewer victims had come forward.
Women fear the new law means their partners will get criminal records, Judge John Platt told the paper.
In a paper drawn up for Sir Mark, he said that figures extrapolated from six courts across the country suggested there had been a drop by 25% in the number of victims who had sought non-molestation orders - equivalent to 5,000 a year.
"Either offenders have changed their behaviour - which seems extremely unlikely - or the victims do not want to criminalise the perpetrators," he told the newspaper.
"It is obviously very worrying."
However, the Ministry of Justice said Home Office statistics showed an increase in the reporting of domestic violence.
It said this was "testament to the growing confidence victims have that they will be listened to and their reports effectively investigated".
Changes in the legislation meant breaching the orders is now a criminal, rather than a civil, offence.
Offenders can be jailed for up to five years.
A spokesman for Sir Mark said: "The president is very concerned that, for whatever reason, the legislation appears to have led to a reduction rather than an increase in the protection afforded to victims of domestic violence as a result of the change of the law."
A Ministry of Justice spokeswoman said it was seeking an urgent meeting with Sir Mark Potter to discuss his concerns.