Damage to a statue of Argentina’s patron saint, the Virgin of Lujan, was discovered in the cemetery near Darwin, which contains the graves of 237 soldiers killed during the Falklands War in 1982.
Foreign Office minister Sir Alan Duncan expressed his concern over the incident and welcomed an investigation by the Falkland Islands Government and police.
He tweeted: “Appalled to hear of act of vandalism at Darwin Cemetery in Falkland Islands. Welcome urgent response & investigation by FIG.”
The vandalism has been condemned by Argentina’s government, which sent a note to the British embassy in Buenos Aires asking the UK government to launch an investigation.
Argentina, which calls the Falkland Islands “Las Malvinas”, lost 649 soldiers in the conflict.
Some 255 British personnel died during the successful defence of the archipelago.
In December, Britain and Argentina agreed a deal to identify 123 Argentinian soldiers buried in the cemetery in Darwin.
At present, their plots are marked “soldier only known to God”.
The Argentine foreign ministry said in a statement that the vandalism was “particularly regrettable” given the pact made last month.
In 2012, the glass case of the cemetery’s statue of the Virgin of Lujan was found smashed.
Cesar Trejo, head of a group of families of Argentine war dead, said the damage appeared to be “caused by bullets”.