Pakistan will undertake a short limited-overs tour in December and January.
The last series between India and Pakistan in either country was in 2007-2008 when Pakistan visited India.
Ties between the two countries' cricket authorities were hit by the 2008 Mumbai attacks, in which 175 people died.
The attack was blamed on a Pakistan-based militant group.
The South Asian rivals continued to play each other on overseas grounds, with their last match taking place in the ICC Twenty20 Cricket World Cup in Sri Lanka in September.
"We will happily host 3,000 Pakistani cricket lovers for the matches. This is the first time that we have decided to issue so many visas in one go," an unnamed official in the interior ministry told the AFP news agency.
The forthcoming series in India will feature three ODIs and two Twenty20s.
The games will be played in Chennai, Delhi, Calcutta, Ahmedabad and Bangalore between 25 December and 6 January 2013.
Reports say that a third of the visas will be given to fans attending the one-day game in Delhi, while 500 visas each will be given to fans going for the games in Bangalore, Chennnai, Ahmedabad and Calcutta.
Correspondents say the move to resume cricketing ties is a sign of improving relations between the two countries.
India is likely to issue 3,000 visas to Pakistani cricket fans attending their team's first cricket series in India for five years, reports say.