In Stockholm, hundreds of fans lined up all day at the Grona Lund amusement park to see Mr Depp perform with his band, the Hollywood Vampires.
Boycott appeals were launched on social media after Ms Heard, who filed for divorce in Los Angeles last week and appeared in court with a black eye, accused the Oscar-nominated star of assaulting her.
But the calls appear not to have been heeded by many.
Grona Lund "is opposed to all kinds of violence - especially domestic, but he has not been proven guilty so we cannot hold him responsible for a crime he has not been found guilty of," spokeswoman Annika Troselius told AFP.
Ms Heard, 30, submitted pictures to the court showing a bruise on her face that she claims was inflicted during a fight on May 21 and said she feared the 52-year-old Pirates of the Caribbean star might harm her.
A judge subsequently imposed a temporary restraining order on Mr Depp, ordering him to stay away from Ms Heard.
But now some close to Mr Depp - including daughter Lily-Rose and former longterm partner Vanessa Paradis - are speaking out in support of the actor.
Lily-Rose, 17, posted a photo on Instagram apparently showing herself as a baby, with Mr Depp holding her hands and helping her walk.
Celebrity news website TMZ posted a photo of a handwritten letter that it said it obtained from Ms Paradis, in which she describes her former partner as "a sensitive, loving and loved person."
"I believe with all my heart that these recent allegations being made are outrageous, in all the years I have known Johnny, he has never been physically abusive with me and this looks nothing like the man I lived with for 14 wonderful years," the note read.
The letter dated Friday is signed by Ms Paradis, who is also the mother of Mr Depp's son Jack.
Ex-Wife Weighs in
Others coming to Mr Depp's defense include famed actor, director and Monty Python alum Terry Gilliam.
Mr Gilliam commented as he retweeted a column by standup comedian Doug Stanhope, who referred to Mr Depp as a friend and wrote that he has known him for a few years.
Like many of Johnny Depp's friends I'm discovering that Amber is a better actress than I thought.. if only the... https://t.co/QJ9S65nvhQ? Terry Gilliam (@TerryGilliam) May 30, 2016
In the column, published Sunday by entertainment website The Wrap, Mr Stanhope wrote that he and his girlfriend were at Mr Depp's house on May 21 just before the alleged assault.
The actor told them "Amber was now going to leave him, threatening to lie about him publicly in any and every possible duplicitous way if he didn't agree to her terms."
Also weighing in was Lori Anne Allison, who was married to Mr Depp in the Eighties, celebrity news website TMZ reported.
Ms Allison reportedly told the site that she doesn't believe Ms Heard's allegations and referred to Mr Depp as a "soft person."
In a sworn statement, Ms Heard - who is seeking spousal support - said Mr Depp was verbally and physically abusive to her during the entirety of their relationship. The two have been married for nearly 16 months.
She added that Mr Depp has a "totally acknowledged public and private history of drug and alcohol abuse," and that she was scared of his temper.
TMZ published a picture showing Ms Heard with bruising around her right eye, reporting that the actress says it was taken shortly after Depp hurled his iPhone at her face on the evening of May 21.
After reviewing dozens of pages of evidence, Los Angeles Superior Court Judge Carl Moor ruled that Mr Depp was banned from coming within 100 yards (91 meters) of Ms Heard. The order will be reviewed on June 17.
The Hollywood Vampires performed in Germany on Sunday and were due to play in Denmark on Tuesday, followed by the Romanian capital Bucharest on June 6. A series of US concerts are scheduled for July.