The fund was set up following the blaze at the block of flats in West London in the early hours of Wednesday morning, which has so far claimed the lives of 30 people - a toll that is expected to rise in the coming days.
Brentford play their home games nearby at Griffin Park and will use the July 22 encounter with Southampton to generate further funds, donating profits from ticket sales and also putting on other fundraising activities on the day.
"The club is situated relatively close to the site of the disaster, and we wanted to do something to support our community and those affected," chief executive Mark Devlin told the Bees' official website.
"Brentford is very much a community club and I'm delighted that Southampton have joined with us in donating the profits from the ticket sales of our friendly match.
"We also anticipate there will be other fundraising activities on the day and we hope that as many fans as possible will be able to attend the game, so that we can raise as much as possible."