The National Gallery's East Wing was evacuated and closed for two hours following the incident, which took place at a spot featured in the 2012 James Bond film Skyfall.
Commonly referred to as The Morning Walk, Mr and Mrs William Hallett were painted shortly before their marriage in the summer of 1785, when they were both 21, and measures 2.3m by 1.7m.
According to the National Gallery: "William is in a black, silk velvet frock-suit. His apparent carelessness is actually a studied pose. The undone jacket and with one hand tucked into it is a stance seen in many fashionable 18th century informal portraits.
"Elizabeth is in a dress of ivory silk - perhaps her wedding dress - caught at the waist with a black silk band. A frilled muslin kerchief covers her breast, with a knot of grape-green ribbon under it.
"The light, feathery brushstrokes used to describe the landscape are typical of Gainsborough's late style."
The Morning Walk, which sold for £30,000 in 1954 thanks in part to a £5000 Art Fund grant, sits immediately adjacent to An Experiment on a Bird in the Air Pump, a 1768 work by Joseph Wright of Derby, and opposite Joseph Turner's The Fighting Temeraire (1839).
A Metropolitan police spokesman said: "A man has been arrested on suspicion of criminal damage. He was taken to a central London police station where he remains in custody."