Moving in a northwesterly direction at about 24 km per hour, Ida was about 10 km from the centre of the island and 245 km east of the western tip of the province of Pinar del Rio.
Weather conditions are expected to continue to worsen in western Cuba, while in the capital city of Havana, the rains have gradually intensified.
Earlier on Friday, Cuban president Miguel Diaz-Canel urged people to take precautions in light of the imminent impact of Ida on the island.
"Tropical storm Ida is nearing Cuba. The western territories have prepared to confront it. I ask our people to be disciplined and responsible not to regret the loss of human lives," he said on Twitter.
So far, no casualties have been registered in the country as a result of the hurricane.
Forecasters estimate that Ida, which formed as a tropical storm in the Caribbean on 26 August, is expected to hit the US on Sunday.
The hurricane season in the Caribbean runs from 1 June to 30 November.