The pitch was playable but, as with both of this week's Carling Cup semi-finals, there were safety issues affecting fans and concerns over transport.
Arsenal had an FA Cup tie against Cardiff called off in similar circumstances last February.
A club statement read: "Despite making every effort to stage tonight's match against Bolton Wanderers, the sudden and unpredicted adverse change in weather conditions in the Highbury area has left us no choice but to postpone the fixture.
"We apologise for any inconvenience this has caused and wish to state that this decision was not made lightly and supporters' safety and travel
arrangements were major factors in our thinking.
"The club will announce the revised date for this match in due course and all tickets currently held will be valid for the rearranged fixture.''