The open letter, from the Human Artistry Campaign's Stealing Isn't Innovation movement, demands that the companies engage in "ethical" partnerships, rather than "stealing".
Other signatories include actors Joseph Gordon-Levitt and Olivia Munn, musicians Aimee Mann, MGMT, Common, Cyndi Lauper and Simon Le Bon, as well as author Jonathan Franzen.
The letter says: "America's creative community is the envy of the world and creates jobs, economic growth, and exports.
"But rather than respect and protect this valuable asset, some of the biggest tech companies, many backed by private equity and other funders, are using American creators' work to build AI platforms without authorisation or regard for copyright law.
"Artists, writers, and creators of all kinds are banding together with a simple message: Stealing our work is not innovation. It's not progress. It's theft - plain and simple."
It adds: "A better way exists: through licensing deals and partnerships, some AI companies have taken the responsible, ethical route to obtaining the content and materials they wish to use.
"It is possible to have it all. We can have advanced, rapidly developing AI and ensure creators' rights are respected."
Johansson has previously spoken out against the use of artificial intelligence, after Open AI launched a ChatGPT voice assistant that sounded like her.
She said she was shocked and angered at how "eerily similar" the chatbot was, prompting OpenAI to say it would pausethe use of the voice.
