Pakistan say India's claim they will not visit for next year's Asia Cup could "impact" Pakistan's participation in the 2023 50-over World Cup.
Jay Shah, secretary of the Indian cricket board (BCCI), said the Asia Cup needed to be moved to a neutral venue.
Pakistan's board (PCB) responded with "surprise and disappointment", adding Shah had acted "unilaterally".
The sides do not currently meet outside of international tournaments because of relations between the two countries.
Pakistan are due to host their first Asia Cup since 2008 next year before India will host the 50-over World Cup in October and November. Pakistan are also set to host the ICC Champions Trophy in 2025.
Pakistan last visited India for the T20 World Cup in 2016, while India have not played in Pakistan since the 2008 Asia Cup.
The two teams meet in the Men's T20 World Cup in Australia on Sunday.
Shah, who is also president of the Asia Cricket Council (ACC), the Asia Cup's organiser, said: "The Asia Cup 2023 will be held at a neutral venue.
"I am saying this as ACC President. We [India] can't go there [to Pakistan], they can't come here. In the past also, the Asia Cup has been played at a neutral venue."
This year the white-ball competition was held neutrally in the United Arab Emirates and won by Sri Lanka, with Bangladesh, Afghanistan and Hong Kong also taking part.
The PCB said Shah's comments were made "without any discussion or consultation" with themselves or the ACC board and "without any thoughts towards their long-term consequences and implications."
It added: "The overall impact of such statements have the potential to split the Asian and international cricketing communities, and can impact Pakistan's visit to India for the ICC Cricket World Cup 2023 and future ICC events in India in the 2024-2031 cycle.
"The PCB has to date not received any official communication from the ACC on the statement of the ACC President."
"As such, the PCB has written to the Asian Cricket Council to convene an emergency meeting of its board as soon as practically possible on this important and sensitive matter."