The 60-year-old took the Pilgrims to promotion last season but the team have struggled to adapt to the step up.
They almost ended their winless run on Saturday, but a late Eastleigh penalty kick proved to be the end for the respected former Norwich City and Swindon Town defender.
A short club statement said: "Ian took charge at the Jakemans Community Stadium in September 2022, helping to preserve the club's National League North status in his first season at the helm, before guiding the Pilgrims to promotion through the play-offs in May.
"However, a difficult start to life in the National League has led to a change being made."
Boston, who tumbled out of the FA Cup to lower league Gainsborough Trinity 4-0, are next in action with a home game against Dagenham & Redbridge on 9 November.
The club now begin their hunt for a new manager, two years after Culverhouse was given the job.
Following the 1-1 draw at Eastleigh, he said: “I thought we were superb all the way through. We handled their threat and defended really well.
“We looked a threat everytime we got the ball forward. We are a good side but when you are at the bottom you don't get anything, you have to earn everything you get.
“We have to lift them now, they gave everything today."