Law enforcement sources tell editors at TMZ.com, that thieves targeted the Ironic rocker, 42, last Thursday (09Feb17) when she was away from her home in the city's Brentwood district.
Editors at the gossip site report that other items may have been stolen in addition to Alanis' $2 million stash of jewellery.
The Canadian rock star, who became a mother for the second time last year (16), has also been the victim of white-collar crime as in January (16) her former business manager Jonathan Schwartz pleaded guilty to stealing $4.8 million (£3.9 million) from her.
Jonathan, who has also worked with Lady Gaga and Beyonce, admitted taking the cash from the singer over a period of four years. He claimed he also took about $1.7 million (£1.4 million) from other clients.
The rogue business manager's plea deal calls for him to serve a sentence of between four and six years in prison.
Alanis sued his partners at his former company, GSO Business Management, last year (16) but dropped the suit after reaching a settlement.