The budget airline will have thrice-weekly flights using Boeing 737-900ER aircraft on the route, it said.
"The 4,268km route or equivalent to a 5-hour 20-minute flight will signify the airline's furthest destination from its main hub in Kuala Lumpur," the statement said.
Malaysians now going to Punjab have to fly to New Delhi and travel five to eight hours by rail or road to destinations in the state.
The Malindo Air statement said promotional fares for Business Class will start at RM1,309 one-way while the Economy Class fare will start at RM759 one-way, inclusive of light refreshments and a meal, in-flight entertainment and free baggage allowance.
The airline's CEO, Chandran Rama Muthy, said in the same statement: "We are proud to extend our wings further up north of India to Amritsar."
"Malaysians and transiting visitors from neighbouring Singapore can now look forward to a smooth flight to Amritsar via Kuala Lumpur whether for business, leisure or religious purposes," he said.