The 22-year-old had also qualified on the front row for the Belgian GP sprint in July but Japan will be the first time Piastri has started a full grand prix from that position.
"I'm very happy to buy her an airline ticket," Brown told Sky Sports television after Nicole Piastri responded to a jubilant McLaren social media post with the words "anyone got a cheap flight to Japan?"
"So if you can get here Mrs Piastri, we want to see you tomorrow," he added.
Nicole has acquired quite a following on X (formerly Twitter) for her joking comments on Oscar's career.
"What!! So we are doing this for another 3 years???," she wrote this week when McLaren announced her son's contract extension to 2026.
From struggling to score points, McLaren are now looking quicker than engine provider Mercedes. Norris has registered three second place finishes in the last six races.
"He's driving great," Brown said of Piastri. "It's exactly why we signed him up for another three years. I think our driver pairing is awesome.
"The team is really gelling, Andrea [Stella]'s leadership has been fantastic and everyone's doing a first class job and the results are coming.
"It would be nice to get a car or two ahead of Max at the start and give him a bit of a race. I think we can definitely end up with a couple of cars on the podium."
Piastri had upgrades on his car that Norris already benefited from last weekend in Singapore and the Australian said McLaren had also made some good changes following Friday practice.
"It's the first time I've started on the front row for a while. So, it'll be cool. There's only one car ahead to overtake, so I'll try and make that happen," he told reporters.
Piastri will be only the fifth Australian to start a grand prix on the front row in the history of the championship but he was more focused on other statistics.
"There's not been that many Australians in F1, full stop. But yeah, it's of course not a record I'm trying to chase," he said.
"It's nice just to have that success... and in particular so early on in my F1 career. Some people don't get this opportunity in their whole career. So for me to have it in my first six or seven months is a privilege.
"But of course I want to try and be the next Australian to break some other records or be added to those lists. A nice start, but of course, I want to be able to do more."