The call comes after the Prime Minister gave artificial intelligence its own place at the Cabinet table, naming the country's first cabinet-level AI minister.
The mayor says the night-time economy has earned the same recognition.
In the West Midlands it supports around 324,000 jobs, close to one in four of the region's workforce.
Around 100,000 of those are in pubs, restaurants, grassroots music venues, theatres and cinemas.
The mayor says the new minister should sit within the expanded Department for Business, Innovation, Science and Trade - led by Secretary of State Jonathan Reynolds.
Parker (pictured) said: "Andy Burnham understands the night-time economy. He championed it in Greater Manchester with a Night-Time Economy Commissioner - so he knows what it means to a place and the people who live there. He’s previously called for support and relief for the industry, so he gets it.
“Yesterday he gave AI a minister. I'm asking him to do the same for the night-time economy.
“This is one in four jobs across our region. But more than that, it’s the cultural life blood of our places. It gives people somewhere to go, something to do, places to meet.
“The industry has taken a battering from Covid, rising costs and business rates. They need someone in government whose job is to fight their corner.”
The West Midlands Night-Time Economy Commission, set up by the mayor last autumn, reported in May with 25 recommendations for reviving the sector.
Among them was a call for a national champion in government to join up policy on tax, licensing and transport.
The commission also called for later buses and trains, safer streets and stronger support for grassroots venues.
The mayor added: "We're getting on with our part here in the West Midlands - we’ve got a plan to address the challenges locally.
“But a minister in Government would pull the national picture together, so the whole country works to the same plan.
“We need to look out for the thousands of people who make their living after dark - giving our places the vibrance we all love."
