Monday.
Law, who played one test and 54 one-day internationals for Australia, joined as Bangladesh's head coach in July last year on a two-year contract, replacing compatriot Jamie Siddons.
"It is a matter of great regret for us to inform you that our head coach Law has decided to resign from his post in June for family reason," BCB's media committee chairman Jalal Yunus told reporters.
The high point of Law's tenure came at the Asia Cup last month, where hosts Bangladesh defeated heavyweights India and Sri Lanka during the group stage before narrowly losing the final of the four-team tournament to Pakistan.