The male predator, which has killed three people in the past two years, scaled two walls at the wedding venue after being attracted by the noise and lights at the star-studded event, reported Daily Mail online.
It was finally beaten away by guards as it tried to jump a third wall just 50ft from the newlyweds and their 85 guests.
The couple have also adopted a tigress called Machli, with Brand deciding to make it a wedding gift to the 'I Kissed A Girl' hitmaker.
The 25-year-old singer, who already owns a slightly smaller domestic cat called Kitty Purry, will leave Machli to prowl in her jungle home and the money Brand paid for her will be invested in the tiger's welfare and the park's conservation schemes.
Their extravagant wedding ceremony also featured a Hindu guru and a fortune-telling parrot.
The 'A-list' couple tied the knot in a lavish, colourful Hindu ceremony at the Aman-i-khas resort on the edge of the Rajasthani nature reserve with 85 friends and family in attendance.