Workers have scrambled up the 21-metre (70-foot) golden-coloured statue in the eastern city of Kolkata in West Bengal, throwing ropes around its shoulders to secure it.
The sculpture showing the 38-year-old Argentina and Inter Miami star raising the World Cup trophy was unveiled during Messi's so-called GOAT Tour of India in December.
But West Bengal state legislator Sharadwat Mukherjee said it was no longer safe.
"The statue of the Argentine football legend in the city of Kolkata was found unsafe by engineers of the West Bengal government," he said.
"We have noticed that the statue is swaying in the wind."
Workers on Wednesday used ropes to attempt to secure the statue, which looms over a busy road.
Mukherjee said it was not clear when it would be brought down.
"Removal has proved easier said than done," he said. "We are planning to remove the statue at the earliest opportunity."
He did not say whether the statue would be re-erected at another site.
Argentina is set to begin its World Cup campaign on June 16 against Algeria in Kansas City. Messi has not formally confirmed his plans to play in the World Cup, but is widely expected to return for what would be a record-matching sixth appearance at the tournament. He remains the side's talisman for the defence of the title they won in Qatar four years ago.
India - a nation of 1.4 billion - is a cricket powerhouse, but struggles on the football pitch and is 142nd on the FIFA rankings. Football, however, is the country's second favourite sport, according to research by data company Nielsen released on Wednesday.