"He (Shah) is a general secretary of the party and has been a minister in a highly successful state. I think making him in charge is not a crime," Singh told reporters.
The BJP Sunday announced Shah has been appointed in-charge of BJP affairs in Uttar Pradesh for the upcoming Lok Sabha polls.
The former home minister of Gujarat has faced allegations of involvement in the Sohrabuddin staged shoot-out case.
"Modi has not recommended anybody," said Rajnath.
Besides Shah, young leader Varun Gandhi was given the charge of the party's affairs in West Bengal, Rajiv Pratap Rudy of Rajasthan, and Om Mathur of Gujarat.