The US pop star says Meghan is a victim of "the most public form of bullying I have seen in a while".
The singer's comments come after Sir Elton John and US chat show host Ellen DeGeneres commented publicly to stand up for the royal couple.
Harry and Meghan have been criticised by some newspapers for taking four trips by private jet in 11 days, despite campaigning against climate change.
Sir Elton John attacked what he described as "distorted and malicious" accounts of Harry and Meghan's private stay at his home in Nice.
He said he and his husband offered his home in Nice and paid for them to travel by private plane, with an "appropriate contribution to Carbon Footprint" made to support Prince Harry's "commitment to the environment".
Meanwhile, DeGeneres said they were "the most down-to-earth, compassionate people", reflecting on a meeting between her, her wife and the royal couple to discuss their work on wildlife conservation.
She added: "Imagine being attacked for everything you do, when all you're trying to do is make the world better."
Now Grammy Award-winning Pink has asked fans to "be a bit kinder".
She tweeted: "I'm happy to see people coming to the defence of The Duke and Duchess of Sussex.
"The way people treat her is the most public form of bullying I have seen in a while. It's out of control. Let's all be a bit kinder, huh?
"Let's show our children that it's cool to be kind."
On Monday, Harry and Meghan posted a quotation by Archbishop Desmond Tutu on Instagram.
It read: "Do your little bit of good where you are; it's those little bits of good put together that overwhelm the world."