The matter was discussed at the Board's all-powerful Working Committee and it was decided to convey to the ICC the situation prevailing in the country.
BCCI President N Srinivasan said the issue was now for the ICC to decide.
"We have informed the ICC about it. They will have to examine and take a view," he said after the meeting.
Rising tension at the LoC, after Pakistan's violation of the ceasefire, has led to protests by Shiv Sena against the Pakistani players' participation in the ongoing Hockey India League, prompting the Mumbai franchise to send back its Pakistani recruits.
The eight-team Women's World Cup is scheduled to be held entirely in Mumbai between January 31 and February 17 and there is concern that protests might lead to trouble.
The Wankhede Stadium, Cricket Club of India's Brabourne Stadium, the Mumbai Cricket Association's Bandra Kurla Complex ground and the MIG Club in Bandra are the venues for the women's World Cup matches.
The BCCI decided that the best course of action would be to apprise the ICC of the security concerns that have been raised by the Mumbai Cricket Association. MORE