Home Minister Sushilkumar Shinde said he has sent the invite through the diplomatic channel.
"During the visit, the new Indo-Pak visa agreement will be operationalised," he told reporters.
Mr Shinde said Mr Malik's birthday falls on December 12 and he had expressed his desire to spend the day at the Taj Mahal and the government would facilitate his visit to the historic city.
Asked whether Mr Malik's wife would also accompany him, Mr Shinde said "we will welcome his visit with family".
The new liberalised Indo-Pak visa pact replaces a 38-year-old restrictive visa agreement and paves the way for time-bound visa approval and greater people-to-people contact and trade.
The visa agreement, signed by then External Affairs Minister S M Krishna and Mr Malik in Islamabad on September 8, eases curbs on issuing visas to traders, elderly people, tourists, pilgrims, members of civil society and children.
Under the new regime, one can visit five places, instead of the three at present, and those above 65 years of age and children below 12 years of age and "eminent" businessmen are exempted from reporting to the police.
Mr Malik had indicated to Mr Shinde, when they met in Rome on the sidelines of the Interpol General Assembly last month, that he would travel to New Delhi to formally launch the new visa regime.
However, due to the winter session of Parliament, the visit could not materialise. Later, official sources said that as the government was planning to hang 26/11 terrorist Ajmal Kasab on November 21, the visit was put on hold.