Bahrain's Interior Ministry said the woman was killed and her three children injured by shrapnel from what it described as a terrorist bomb attack.
But the Bahrain Centre for Human Rights (BCHR) called the official account into question, saying "there are conflicting narratives regarding the incident ... as well as conflicting accusations concerning the responsibility for this tragic event".
That appeared to be a reference to social media comments by Bahraini opposition activists that people who witnessed the incident had said the woman had accidentally driven into a royal convoy and was then fired upon by the security services, Reuters reported.
The Interior Ministry said in its statement on Friday that it was investigating the incident. Large crowds attended the woman's funeral on Saturday.
The human rights record of Bahrain, which hosts the United States' Fifth Fleet, has been criticized by the international community.
In June, authorities closed down the main opposition group, detained BHCR's president Nabeel Rajab and stripped the island's leading Shiite cleric of his citizenship.