The Flash player plug-in allows multimedia content created using the Flash format to be viewed via a web browser.
Adobe will continue to develop the player for PCs. It will also support Air – a tool which lets developers turn web-based applications using Flash into standalone mobile apps.
The Flash Player had been popular on Google Play – with two-thirds of users giving it a top score.
But Adobe said it was removing the option to install the plug-in because it was likely to exhibit “unpredictable behaviour” when used with the latest version of Android, known as Jelly Bean.
It also suggested that smartphone owners who had upgraded to the latest system should uninstall the Flash Player if it was already on their device.
Although Adobe is no longer actively developing the player for Android, Blackberry or Symbian devices – and never released it for Apple iOS or Windows Phone handsets – it has said it would continue to offer security updates and bug fixes for existing versions until September 2013.
Adobe first offered the Flash Player for smartphones in 2010 but faced a setback when Apple refused to allow it to be installed on iPhones and iPads.
An article published by Apple’s former chief executive Steve Jobs suggested supporting Flash would compromise the reliability, battery life and security of his firm’s products.
Instead he promoted the HTML 5 web standard, urging Adobe to focus on it as an alternative.
YouTube’s decision to encode its videos in HTML 5 also helped speed up the format’s adoption.
When Adobe announced its decision to end development of the mobile Flash Player it acknowledged that HTML 5 had become “the best solution for creating and deploying content in the browser across mobile platforms” and said it would boost its investment in the format.
Adobe’s chief technology officer, Kevin Lynch, told the BBC it was “too theoretical” to speculate about whether its mobile Flash Player would have found more support had it handled its development differently.
But he stressed the firm was still confident about its future on PCs.
“With Flash we’re focusing on two areas,” he said.
“One is console quality gaming – this is really bringing the level of gaming to the web that you can see on consoles today and with Flash we actually reach more people than any of the gaming platforms. That includes working on 3D technology inside the browser.
“The second area is premium copy-protected video for people who have high value video, like movie studios or cable companies, who want viewers to watch the video anywhere but also want to make sure its protected.”
He added that some of these innovations could ultimately find their way to HTML 5 through his firm’s contribution to the Webkit Open Source Project – a web browser engine which renders webpages – and its involvement in the platform’s standards body W3C (World Wide Web Consortium).