How to disable ScalaDoc generation in dist task in Play 2.2.x (using project/build.scala)?

Add the following settings to the Play project:

sources in (Compile,doc) := Seq.empty
publishArtifact in (Compile, packageDoc) := false

With the change it should be as follows:

play.Project(appName, appVersion, appDependencies)
    .settings(scalaVersion := "2.10.3")
    .settings(jsSettings : _*)
    .settings(
        publishArtifact in (Compile, packageDoc) := false,
        publishArtifact in packageDoc := false,
        sources in (Compile,doc) := Seq.empty
    )

Thanks @peter-hilton for the comment!