Drivers will be each be given a one-off cash payment of £1,500, intended to help pay for personal protective equipment and other overhead costs.
Some drivers have criticised the amount on offer, saying it would not go far enough to cover their lost earnings.
Many taxi drivers have suffered a big loss of trade throughout the pandemic.
It has been particularly hard for taxi drivers in the North West where a second lockdown has been in place since Monday, October 5 and has at least another week to run.
Infrastructure Minister Nichola Mallon announced the £14 million support package for the sector last month.
Marking the opening of the scheme, she said applications would be processed quickly and it was planned that the payments would be made before Christmas.
“I hope that this support, along with the additional support of £1.2m which I put in place earlier in the year to waive vehicle licence fees, will enable taxi-drivers to continue working during these exceptionally difficult times,” she said.
Self-employed licensed taxi drivers who worked or were available to work between 22 March and 30 September this year are eligible for the money.
Wedding car drivers can also apply for the scheme, which runs until Friday, November 27.
However, the scheme is not open taxi operators who run depots.