The incident came to light in the morning when the body of the woman was found in a shaft in the accused's residence, police said.
They said several persons were questioned after which the police zeroed in on a man, identified as Naveen Khatri.
During interrogation it emerged that the woman, a final year student at Lakshmibai College under the University of Delhi, was in a relationship with Khatri, who was to get married with someone else, they said.
The police said the accused tried to dump the body somewhere else and also attempted to burn it once, but failed.
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The matter came to light today after neighbours complained of a 'terrible stench' and the police was informed, they said.
The police are also probing the role of other members of the accused's family in the incident.
It has emerged they had objected to their relationship and wanted Khatri to marry another woman, police said.