The attack took place early on Thursday morning in an upscale neighbourhood in the Indian city of Mumbai, where Khan lives with his family.
City police told BBC Marathi that the actor was injured after a scuffle broke out between him and an unidentified man who entered his house sometime after midnight.
Police have formed teams to investigate the matter.
"Khan has come out of surgery and is out of danger. He is currently in recovery and the doctors are monitoring his progress," Khan's team said in a statement.
Speaking to reporters after the surgery, Dr Nitin Dange of Lilavati Hospital, where Khan is admitted, said that the actor "sustained a major injury to the thoracic spinal cord due to a lodged knife in the spine".
"A surgery was performed to remove the knife and repair leaking spinal fluid. Two other deep wounds on his left hand and one other on his neck were repaired by the plastic surgery team," he said.
Khan is married to Bollywood star Kareena Kapoor Khan and the couple have two children. His team said they were safe.
His wife said afterwards on Instagram stories that it had been "an incredibly challenging day for our family", and that they were still "trying to process" it.
She "respectfully and humbly" asked the media and paparazzi to "refrain from the relentless speculation and coverage".
"While we appreciate the concern and support, the constant scrutiny and attention are not only overwhelming but also pose a significant risk to our safety," she added.
"I kindly request that you respect our boundaries and give us the space we need to heal and cope as a family."
The exact details of the assault are not clear yet. Police have said that "an unknown person" had entered the actor's home.
"After that, an argument broke out between Khan and the intruder," Mumbai's Deputy Commissioner of Police Dixit Gedam told BBC Marathi.
Khan's team said it was a case of "attempted burglary" but did not share more details.
"We request the media and fans to be patient. It is a police matter," they said.
Khan, who made his Bollywood debut in 1993, primarily works in Hindi cinema and is known for his quick wit and comic timing.
Among his popular movies are romantic comedies such as Dil Chahta Hai and Kal Ho Naa Ho and recent action dramas such as Tanhaji and Devara: Part 1.
His role as an antagonist in Omkara, a 2006 critically acclaimed adaptation of Shakespeare's Othello, was widely appreciated.
Khan comes from a family of erstwhile Nawabs who ruled Pataudi, a small princely state on the outskirts of Delhi, and is married into a family of film stars.
His father Mansoor Ali Khan Pataudi was a cricketer who captained the Indian team in the 1960s. His mother Sharmila Tagore is a veteran actress who has featured in prominent Hindi and Bengali films from the age of 14.
His sister Soha Ali Khan also acted in films for some years.
Khan's wife Kareena comes from a family of celebrated actors, directors and producers who have been active in Bollywood for almost a century.
The auto-rickshaw driver who rushed Bollywood actor Saif Ali Khan to the hospital after he was stabbed multiple times at his Bandra residence early Thursday has shared details about the incident.
Speaking to ANI, the driver shared that he saw a woman trying to hire an auto-rickshaw at 2 am on Thursday. Soon after he approached the scene, he saw the ‘Hum Tum’ actor covered in “blood,” coming out of the gate, accompanied by a few others.
The actor was “bleeding” from his “neck and back,” the driver said.
“I drive my vehicle at night. It was around 2-3 a.m. when I saw a woman trying to hire an auto, but nobody stopped. I also heard calls for a rickshaw from inside the gate. I took a U-turn and stopped my vehicle near the gate. A man covered in blood came out, along with 2-4 others. They put him in the auto and decided to go to Lilavati Hospital. I dropped them there, and later I came to know that he was Saif Ali Khan. I saw him bleeding from his neck and back,” Rana told ANI.
When asked if the police had called him to give a statement, Rana said, “No.”
Earlier, Saif’s staff members were brought to the Bandra Police Station for questioning regarding the case but were later allowed to leave.
The Mumbai Police has clarified that no arrests have been made so far, and the investigation is ongoing.
The actor is currently admitted to Lilavati Hospital and is being treated.
Saif was attacked by an intruder in his 11th-floor Bandra flat in the early hours of Thursday. The incident occurred when the intruder allegedly confronted the actor’s maid at his residence. As Saif attempted to intervene, the situation escalated into a violent altercation, resulting in the actor sustaining several stab wounds.
Saif underwent surgery at Lilavati. According to the doctors, Saif sustained a major injury to the thoracic spinal cord due to a knife lodged in his spine, and surgery was performed to remove a 2.5-inch-long blade from the actor’s spine and repair his leaking spinal fluid.
While Saif is “out of danger,” doctors are continuing to monitor him.
