It is giving away 15,000 free seats – for immediate booking online - the budget carrier said in a media statement on Friday.
Jetstar’s offer ends on Tuesday.
Whichever airline they choose, travellers will have to pay taxes and other surcharges that come to about $120 for a round trip.
It is still a fraction of what it now costs to fly Singapore Airlines and Malaysia Airlines that currently dominate the market and charge more than $400 for a round trip.
Low-cost carriers that have for years been kept out of the Singapore-KL market will start plying the route from Feb 1.
For a start, Tiger which operates out of the budget terminals at both Changi Airport and Kuala Lumpur International Airport, and Jetstar which flies to the main terminals, will each operate one service a day between the two points.
Malaysian budget carrier AirAsia is expected to announce details of its Singapore-KL service at a press briefing in Singapore on Thursday.
The partial liberalisation of the market comes after years of lobbying from the airlines and travellers on both sides of the Causeway.
By December, all restrictions will be lifted, which means low-cost carriers can fly as many times as they want between Singapore and KL.
Tiger’s chief executive officer Tony Davis said the airline will also continue to push for the rights to fly to other cities in Malaysia including Penang and points in East Malaysia.
Jetstar, in the meantime, is so pleased with the response to its 88-cents Singapore-KL promotion fare that the airline is rewarding customers with a buy-one-get- one free offer for flights to all its 14 destinations, said chief executive officer Chong Phit Lian.
Bookings must be made online at www.jetstar.com/specials/1+1 between Jan 9 and 11 for travel until Feb 3.