The couple have released a statement through Archewell - their foundation - to share their issues about Spotify and to "ensure changes to its platform are made to help address the public health crisis".
The pair signed a lucrative deal with the streaming giant to host and produce podcasts, estimated to be worth around 25 million US dollars (£18 million), in late 2020.
The statement comes as Spotify faces a backlash for hosting a podcast by comedian Joe Rogan who uses the platform to promote anti-vax views - including a suggestion that the young and healthy should not get jabbed.
It led to musician Neil Young telling Spotify to remove his music from the platform, as he claimed the streaming service risked people's health by allowing fake information about vaccines to be circulated.
Singer Joni Mitchell also removed her music from Spotify and said she was standing “in solidarity” with Neil Young.
The Grammy award-winning singer said in a statement the streaming giant was allowing “irresponsible people” to spread lies that were “costing people their lives”.
Spotify is now facing even more pressure, as Harry and Meghan have waded into the row and the streaming giant risks losing even more artists from its platform.
An Archewell spokesperson said: “Since the inception of Archewell, we have worked to address the real-time global misinformation crisis. Hundreds of millions of people are affected by the serious harms of rampant mis- and disinformation every day.
"Last April, our co-founders began expressing concerns to our partners at Spotify about the all too real consequences of COVID-19 misinformation on its platform.
"We have continued to express our concerns to Spotify to ensure changes to its platform are made to help address this public health crisis.
"We look to Spotify to meet this moment and are committed to continuing our work together as it does.”
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Spotify acquired The Joe Rogan Experience podcast in 2020, reportedly for more than 100 million dollars (£77m) and it is reportedly downloaded almost 200 million times a month.
Following Young’s reported concerns Spotify said it aimed to balance “both safety for listeners and freedom for creators” and had removed over 20,000 podcast episodes related to Covid misinformation since the start of the pandemic.