On May 6, Mr Khan was convicted by the sessions court for culpable homicide not amounting to murder and sentenced to five years in jail.
On May 8, the High Court granted him bail and suspended his sentence pending the hearing and disposal of his appeal against the conviction.
The High Court had also said that the actor would need to seek the court's permission every time he wanted to leave the country.
Mr Khan's application, filed today, says that he wants to travel to Dubai for a show on May 29. A vacation bench of the High Court is likely to hear the matter next week.
A man was killed and four others were wounded when Mr Khan's Toyota Land Cruiser ran over them while they were asleep on a pavement outside a bakery in suburban Bandra on September 28, 2002.