The spokesmen for the party, which leads the ruling coalition, did not disclose details about the ailment of their 64-year-old leader, widely regarded as the country's most powerful politician, although Manmohan Singh is prime minister.
Party spokesman Janardhan Dwivedi told reporters Gandhi had been "recently diagnosed with a medical condition that requires surgery," and that on the advice of her doctors "has traveled abroad, and she is likely to be away for two to three weeks." He did not say where she would be receiving her treatment.
Sonia Gandhi is the widow of former Prime Minister Rajiv Gandhi, who was assassinated in May 1991.
Sonia Gandhi's surgery was expected to be performed this week. The Times of India reported it had learned the surgery was done Thursday and that it was successful.
She was accompanied by her son Rahul, and daughter Priyanka, the Hindustan Times reported.
The Congress Party-led coalition and Singh are under political pressure from the opposition in Parliament for a number of alleged corruption scandals and the current state of the Indian economy, hobbled by a sharp rise in prices and stubborn high inflation.
Before leaving, Gandhi appointed a four-member team to look after the affairs of the party during her absence. The team includes Rahul Gandhi, Indian Defense Minister A.K. Antony, her political secretary Ahmed Patel, and Dwivedi.
On Gandhi's medical condition, or when she left India, Manish Tewari, another party spokesman, said: "Public personalities are entitled to a certain amount of privacy, especially when it concerns a medical condition," and urged reporters to show "sensitivity, circumspection and discretion," The Hindu newspaper said.