Farook and his wife killed 14 people in the California city last December before police fatally shot them.
A court order demands Apple help circumvent security software on Farook's iPhone, which the FBI said contains crucial information.
The BBC understands Apple will contest the order.
Since a software update released in September 2014, data on Apple devices - such as text messages and photographs - have been encrypted by default.
It means if a device is locked, only the passcode can be used to access the data. If 10 incorrect attempts at the code are made, the device will automatically erase all of its data.
No-one, not even Apple, is able to access the data - a move the company, like several other tech firms in Silicon Valley, made following the Edward Snowden revelations into government surveillance. Read more on bbc.