Senator Brandis wrote to the Senate President Scott Ryan on Thursday to request the referral, while suggesting the under-pressure Labor senator may have breached paragraph 6(3) of the privileges resolutions.
The referral follows Fairfax Media revelations that Senator Dastyari gave counter-surveillance advice to Chinese Communist Party-linked political donor Huang Xiangmo that his phone was probably tapped by government agencies when the pair met last year.
That meeting occurred more than a month after media reports in early September that ASIO's top spy, Duncan Lewis, had warned Labor "that some of their donors had strong links to the Chinese Government".
In addition, Fairfax Media revealed last week an explosive tape recording that showed for the first time that Senator Dastyari delivered a scripted, deliberate and detailed defence of the Chinese government's aggressive land grab in the South China Sea.
Paragraph 6(3) states that: "a senator shall not ask for, receive or obtain, any property or benefit for the senator, or another person, on any understanding that the senator will be influenced in the discharge of the senator's duties".
It states that a senator should not enter into a contract, understanding or arrangement which could have the effect of "controlling or limiting the senator's independence or freedom of action as a senator, or pursuant to which the senator is in any way to act as the representative of any outside body in the discharge of the senator's duties".
Referral to the eight-senator privileges committee is a serious matter as the committee investigates conduct which could obstruct the work of the Senate.
The committee has the power to call witnesses and it
can impose a prison sentence of up to six months, or a fine of up to $5000 for an individual if it believes an offence has been committed.
A final decision on the referral of Senator Dastyari will probably be delayed until early in 2018, as Parliament was due to finish sitting for the year on Thursday evening.
The Turnbull government has attacked Bill Shorten and Labor all week over Senator Dastyari's actions, pressing for the backbench senator to quit the Parliament.
The story Brandis asks for Dastyari referral to powerful privileges committee first appeared on The Sydney Morning Herald.