The portrait by 18th century artist Joshua Reynolds was attacked shortly before the gallery closed Wednesday by a man who smashed the protective glass and drove the hammer into the canvas, The Independent reported Friday.
A gallery spokesman said officials were unsure of restoration costs.
"Until the painting has been professionally assessed by a qualified painting conservator, it is not possible to give a reasonable assessment of the cost of repair," the spokesperson said. "The good news the painting is repairable and is already being looked at."
A man surrendered without incident to security staff, who held him until police arrived. Metropolitan Police said they charged Mark Paton, a 44-year-old homeless man, with one count of criminal damage and another count of possessing a hammer with intent to cause criminal damage.