Johnson founded the team in his own name over 40 years ago, with Story now its CEO and chairman.
Herrod, a notable Ford performance tuner, is an advisory board member of the Ford team.
It comes in the wake of two key Australian motorsport figures in John Bowe and Neil Crompton being diagnosed with the cancer.
Herrod and Johnson have also previously battled the cancer.
"One in six men will be diagnosed with prostate cancer by the age of 85, and it doesn’t discriminate,” Story said.
"We’ve seen a number of key personalities in the motorsport community diagnosed in the past and recent months.
"Thanks to the fantastic work of organisations like The Prostate Cancer Foundation of Australia, the survival rate has increased from 60 per cent to 95 per cent in the past 35 years.
"A simple blood test to check PSA levels can lead to early detection, and that saves lives.
"The Shell V-Power Racing Team has been supporting The Prostate Cancer Foundation for some time by donating the proceeds from the sales of our signed Sierra memorabilia prints, and there’s more to come.
"Our mission is to ensure they can continue the fight against the second deadliest cancer in men in Australia."
The challenge involves 45 sit-ups per day during Men’s Health Week in mid-June.
"Unfortunately, when prostate cancer first develops, there are often no symptoms; they tend to develop in the later stages,” five-time series champion Johnson said.
"It’s why regularly seeing your doctor when you’re over 50, or over 40 if there have been cases in your family, is so important.
"Rob and I were lucky we were diagnosed early, but it’s so important for men to discuss their individual risks and detection options with their doctor.
"When it comes to the Sit-Up 45 challenge, I think I’ll enlist the help of our super-fit crew to do my share.”
PCFA CEO Jeff Dunn added: "The Shell V-Power Racing Team is one of Australia’s oldest and most successful sporting teams, backed by tens of thousands of men who face a one in six risk of prostate cancer in their lifetime.
"We are tremendously proud to have Dick Johnson, Ryan Story, and Rob Herrod supporting our new Sit-Up 45 Challenge.
"45 Australian men will be diagnosed with prostate cancer every day - including men like Rob Herrod and Dick Johnson - we’d welcome all Supercar fans to join the Shell V-Power Racing Team in the Sit-Up 45 Challenge to help us save their lives."
Men’s Health Week will be held across June 14-20.
The Repco Supercars Championship field will return to Victoria for the Winton SuperSprint across May 28-30. Tickets are available here.