Besides downloading the Java app, you can play Minecraft in the browser through an applet at https://minecraft.net/play.
So no, if you are not running Java in the browser, a malicious web page can't run neither Minecraft nor other Java apps that you have locally installed.
Besides downloading the Java app, you can play Minecraft in the browser through an applet at https://minecraft.net/play.
So no, if you are not running Java in the browser, a malicious web page can't run neither Minecraft nor other Java apps that you have locally installed.