Initial reports claimed Ali, who works as a fundraiser for several organisations including one helping the children of Chernobyl, had broken a leg when the quad bike toppled over. That was later denied.
The accident made the front page of the Inside Costa Rica newspaper, which said she had been airlifted to the CIMA hospital in Escazu after she took a tumble on the beach. Bono reportedly accompanied her to the hospital.
Merciela Retana, a spokesperson for the hospital, said last night that they could not provide information on the condition of any patients.
According to Costa Rican immigration reports, both Bono, 53, and Ali, 52, arrived at Juan Santamaria Airport on Feb 11 and have been there ever since.
According to local reports, Ali suffered broken ribs after the quad bike sent her flying.
Other celebrities who have suffered injuries from these bikes, which are mainly used by farmers on their properties, include former rocker Ozzy Osbourne, who was seriously injured after an accident on one at his English country estate several years ago.
A spokeswoman for U2’s London-based publicist Regine Moylett said: “Ali had an accident while on a family holiday in Costa Rica. She sustained a couple of broken ribs, some cuts and bruises, and is recovering well.”
The couple have four children, but it has not yet been revealed how many of them were holidaying with them. They have two young boys of school age and two grown-up girls, who are both studying in New York.
Members of the Hewson family spent much of 2012 touring the world after Bono found himself with time off due to a prolonged period of inactivity with U2. The band were not touring and were only occasionally at work in the recording studio. A new album is reportedly due for release later this year.