The Cricket Club of India, among the country's oldest clubs, also joined calls for the national team to stay away from the June 16 match in Britain, as Indians accused Pakistan of not doing enough to stop militants from operating on its soil.
Pakistan has denied any involvement in the suicide attack on a military convoy that killed 40 paramilitary police last week, the bloodiest loss by Indian security forces in decades.
"Let's boycott Pakistan in @ICC Cricket World Cup! Let's stand together against the terrorism they are sponsoring," cricket fan Ishan Datta said in a tweet.
The International Cricket Council (ICC) governs world cricket.
Another Indian cricket supporter said India's cricket body, one of the world's richest, should use its influence to force Pakistan out of the ICC.
"Either India will be part of World Cup 2019 or Pakistan. You have enough funds to pull this off," the supporter tweeted.
India and Pakistan have not hosted a cricket series between their countries since 2013 due to political tensions.
However, the national teams have faced each other in tournaments such as the 2017 Champions Trophy and 2018 Asia Cup held in neutral venues.
Reuters could not immediately reach Amitabh Choudhary, the acting secretary of the Board of Control for Cricket in India (BCCI), which manages Indian cricket, for a comment on the calls for a boycott.
The Cricket Club of India (CCI) said it supported a boycott of Pakistan at the World Cup in June.
"Though CCI is a sporting association, nation comes first, even before sports," Suresh Bafna, its secretary, told Reuters partner ANI.
In CCI's Mumbai office, a cloth had been placed over a portrait of former Pakistan captain and current Prime Minister Imran Khan, ANI and other media reported.
Photographs of Pakistani cricketers were removed from inside a cricket stadium in the northern Indian state of Punjab, which borders Pakistan, Indian media reported.
Prime Minister Narendra Modi, who faces an election that must be held by May, has promised a strong response. Pakistan has recalled its ambassador to India for consultations amid escalating tensions.
Coverage of the Pakistan Super League (PSL) Twenty20 competition has been blacked out in India.
Event management company IMG Reliance decided against showing the matches live, and Indian television channel D-Sport suspended coverage of the Twenty20 league.
The Pakistan Cricket Board (PCB) expressed "extreme disappointment" on its website.
"Denying India cricket fans the right to follow PSL ... as well as covering or removing portrait of former Pakistan cricket captain and Prime Minister Imran Khan and other legendary cricketers from one of the most historic cricket clubs and venues are highly regrettable actions," PCB Managing Director Wasim Khan said.
The PCB said it would take up the incidents at the ICC committee meeting in Dubai later this month.