Dr Bari, who took over from Sir Iqbal Sacranie as secretary general in June, was visiting the Al-Hikmah centre in Batley as part of a five-day tour of West Yorkshire which will take in parts of Dewsbury and Leeds.
He said the council had been in close contact with the police during the lead up to the arrests.
Speaking exclusively to the Yorkshire Evening Post, the former high school science teacher and father-of-four said: "My reaction is one of awe and surprise. After 7/7, we did not think something like this would come again.
"It is difficult for us to comment at this stage. We do not know who has done this.
Discreet
"The presumption is that it is British born Asians.
"If they are shown to be Muslims and proven guilty then it's a real shock. We have to wait now for the investigation to take place."
Dr Bari said they had been kept informed of events by the police in a bid to avoid the kind of backlash which followed raids on a house in London earlier this year.
He said: "We have been talking to the police. They assured us in a very discreet way that there would be no raid or doors broken down as there was in Forrest Gate. We have learned from that incident."
At a time when the Muslim faith is rarely out of the news, Dr Bari outlined a bold vision for the future and said plans were already afoot to engage further with Asian youths living in Leeds.

• Read his full interview in tomorrow's Yorkshire Evening Post.