"His statement (linking BJP and RSS to Hindu terrorism) is irresponsible and reflects his immaturity," Mr Kumar told reporters.
Mr Kumar, who is senior leader of Janata Dal (United), said that Mr Shinde should realise that he is Home minister of the country and not merely a Congress leader.
"As a Congress leader one can make any statement suitable to party but he (Shinde) should realise that he is Home Minister of the country and should speak on such issues in that capacity and not merely as a Congress leader," the Bihar chief minister said after paying respect to Netaji Subhash Chandra Bode on his anniversary.
Mr Kumar said he if he (Shinde) has any information or documents in support of his charge against BJP and RSS he should initiate action.
"The irresponsible statement of Mr Shinde (on BJP and RSS) reflects his immaturity," he said adding such things sends a wrong message in the society and vitiate the environment.
Addressing the Congress meeting at Jaipur on Sunday, Mr Shinde had said, "...we have got an investigation report that be it RSS or BJP, their training camps are promoting Hindu terrorism. We are keeping a strict vigil on all this."