Shakib's mother and sister were inside the three-storey house in the western district town of Magura when several motor-cycle riders stopped and threw stones at the house on Friday evening, local police chief Proloy Chisim said.
"The stones broke one window of the house. His father spoke to me after the incident and we have already stepped up security in the area," he told AFP.
Shakib's father Mashrur Reza told reporters that a number of windows were shattered on the first floor, including those of the captain's room.
Bangladesh, one of the three co-hosts of the World Cup, were bowled out for their lowest one-day-international total 58 on Friday to leave them facing a huge struggle to secure a place in the World Cup quarter-finals.
Fans also stoned the bus carrying the West Indies team as the players were leaving Sher-e-Bangla stadium after the match in what police claimed was a case of mistaken identity.
Police said fans thought it was the Bangladeshi team bus and they hurled stones at it, shattering two windows.
Police and the elite Rapid Action Battalion have arrested 38 young men in connection with the attack.
"We have filed cases against them and they have been sent to the court," police sub-inspector Abdur Razzak said.
Up to 3,000 fans also torched Bangladesh jerseys and held protest marches on the Dhaka University campus to vent their anger at the loss.
Shakib said it was his worst performance but has insisted his side's World Cup campaign was not over.
Bangladesh's score was worse than their previous low of 74 against Australia in Darwin in 2008 and was also the fourth lowest total in World Cup history.
The World Cup co-hosts, with one win from three games in Group B, face England, South Africa and the Netherlands in their remaining group matches.