The victim, who received injury on her neck, was rushed to a nearby hospital where she is said to be out of danger, they said.
According to Tilak Nagar police, the woman had left her unemployed husband a few months ago as he used to allegedly often beat her and their two children under the influence of alcohol.
Furious over this, the accused slashed her neck when he spotted her near the railway station.
He was apprehended by passersby and handed over to the police.
On Monday last, a 25-year-old woman pursuing Chartered Accountancy was stabbed by a man at a bus stop in Dadar near central Mumbai.
The victim, with her face covered by a scarf, was standing at the bus stop when she was attacked by a man, who mistook her as his wife whom he wanted to kill over some family dispute, police said.
As per statistics available with the police on crime against women, 213 rape cases were registered in Mumbai till now in 2012 as against 215 last year.
Deputy Police commissioners in the metropolis have been instructed to personally look into the crimes against women.