A police spokesman said other suspects had been identified from CCTV footage.
The student and a male friend she was travelling with were beaten, stripped and thrown out of the bus in the attack on Sunday evening.
The attack has sparked outrage in Delhi, which is often seen as unsafe for women.
The capital's rape figures are higher than for other Indian cities of comparable size, correspondents say.
The woman and her friend had boarded the bus from Munirka area and were on their way to Dwarka in south-west Delhi.
They were returning after watching a film in a shopping centre in south Delhi, police said.
The couple were attacked by "at least four men", police said.
The couple have been admitted to hospital, where the woman is said to be in a critical condition.
On Monday, senior police officer Chhaya Sharma appealed to the public to help identify the owner of the bus.
Delhi Chief Minister Sheila Dikshit has promised "strict action" against those responsible.
Indian police have arrested a bus driver in connection with the gang rape of a 23-year-old student on a city bus in the capital, Delhi.