A very brief statement was posted on Celtic Frost's website states the following:

"Celtic Frost singer and guitarist Tom Gabriel Fischer has left Celtic Frost due to the irresolvable, severe erosion of the personal basis so urgently required to collaborate within a band so unique, volatile, and ambitious."

UPDATED on 11 April (thanks to SlaytallicA):

Celtic Frost singer and guitarist Tom Gabriel Fischer talks about his departure from the band. Here's his statement:

"I am devastated beyond description, and I am infinitely disappointed. As the one member of Celtic Frost who is exposed most dramatically to the feedback by our audiences and the media, I feel troubled and humiliated about being unable to honor the enormous goodwill extended to Celtic Frost during the past few years and meet the justified expectations of our fans.

I have always seen the Monotheist album as a mere beginning, and a tame one at that. My mind and spirit are full of energy, creativity, and ideas. Celtic Frost had become the unreserved focus of my life for the second time. I was looking forward immeasurably to working on the next Celtic Frost album. To me, it needed to be darker, heavier, and more experimental than Monotheist.

And yet, Celtic Frost consisted of three individuals, and I was only one of them. In the end I had to concede to myself that there was no other option.

My friendship with and respect for Martin Eric Ain remain unaffected. Moreover, I am in the process of assessing my options to eventually complete, record, and release some of the ideas I originally created for Celtic Frost and the planned next album in the course of the past few years, and to take our distinctive music out on the road again.

There is no way back."

Source:	celticfrost.com
Band profile:	Celtic Frost