Locals discovered the bodies of the deceased, who were believed to be in their 20s, in a public park in Sonipat.
The bodies, which have not been identified, have been sent for post mortem, police say.
Hundreds are killed each year in India for falling in love or marrying against their families' wishes.
Police said the man's legs had been chopped off and put inside the trunk. The woman was found wearing glass bangles, which are traditionally worn by newly-married women.
"It appears they were strangled and dumped here later. They are yet to be identified," senior police officer Praveen Kumar told AFP news agency.
"It seems like a case of honour killing because the woman is wearing wedding bangles but we are not ruling out other motives."
Monday's incident comes days after the state police arrested a man on suspicion of killing his teenage daughter over her relationship with a boy from another caste.
Most parents in India still prefer arranged marriages within their own caste and relationships outside of the caste are frowned upon.
In 2011, India's Supreme Court said those involved in honour killings should face the death penalty.
The naked bodies of a man and woman have been found inside two trunks in India's Haryana state in what police suspect is a case of "honour killing".