Parliamentary Standards Commissioner Daniel Greenberg will carry it out.
Leaked messages from 2021 show Mr Brine had been "trying for months" to contact health bosses while acting as a paid consultant for Remedium Partners.
The MP, who chairs the Commons health committee, said he was responding to a call from ministers to help the NHS during the Covid pandemic.
Mr Brine has yet to comment on Mr Greenberg's inquiry.
The WhatsApp texts show Remedium wanted to supply the NHS with anaesthetists.
In a statement last week to The Daily Telegraph, which published the messages, Mr Brine said he had been "responding in the national interest" during a "national crisis".
"Ultimately, it led nowhere let alone secure any business for Remedium," he added.
The texts were some of the more than 100,000 WhatsApp messages involving former Health Secretary Matt Hancock that were leaked to the newspaper by journalist Isabel Oakeshott. The messages have not been seen by the BBC.
In an exchange from 2 February 2021 published by the Telegraph, then Cabinet Office Minister Michael Gove forwarded a message he said he had received from Mr Brine to Mr Hancock.
In his message to Mr Gove, Mr Brine wrote: "Sorry to raise this but having tried the Dept of Health (seemed logical) and the Chief Exec of [NHS England] (ditto) I am at a loss."
"I have been trying for months to help the NHS through a company I am connected with - called 'Remedium'," he added.
"They have 50 anaesthetists right now who can be in the country and on the ground in the NHS if someone only said let's us help. They just want to assist and asked me how they might.
In the message, Mr Brine said that he had "had nothing," adding this was "despite the PM telling the [Commons] Liaison Committee this is his biggest problem".
"How might I progress this or does the NHS just not need the help?" he added.
Mr Hancock is shown responding to Mr Gove that Mr Brine had not texted him, before later replying: "This is already in hand. Thanks for pinging on."
Mr Brine, the MP for Winchester, was a junior minister at the health department between June 2017 and March 2019. He has chaired the Commons health select committee since November.
The parliamentary register of interests show he was paid £1,600 a month as a "strategic adviser" to Remedium Partners from July 2020. He held the role until December 2021, 10 months after his message to Mr Gove.
The rulebook for MPs says they should not lobby - try to influence - ministers on behalf of companies that are paying them.
A breach of the ban on paid lobbying led to the resignation from the Commons of former cabinet minister Owen Paterson in November 2021.
Separately, the appointment rules for former ministers say they should not lobby the government within two years of leaving their ministerial post.
Labour Party chair Anneliese Dodds, who referred the matter to the Standards Commissioner, said the allegations were "very serious" and the public were "rightly sick of this constant slew of Conservative sleaze".
Liberal Democrat health spokesperson Daisy Cooper said Mr Brine should step down from the health committee while the investigation takes place.
"It is absurd for an MP who may have wrongly lobbied the NHS to now be in charge of holding them to account. The evidence against him looks damning and is clear for all to see."
When approached by the BBC last week, the health department said it did not comment on leaks.
Mr Brine has previously been reprimanded by Acoba, the watchdog that oversees appointment rules, for inviting then-vaccines minister Nadhim Zahawi to take part in an event in 2021 hosted by a different company, Sigma Pharmaceuticals, where he was a paid adviser.
Acoba also criticised him for failing to inform them he was taking up the role with Sigma until after it started, something he blamed on "poor admin on my part".