Police Scotland said Peter Murrell, the former party chief executive, had been arrested for a second time earlier on Thursday.
Peter Murrell, the party's former chief executive, was first arrested in April last year and was released without charge.
The SNP chief said his position was "untenable" following last night's Commons chaos.
The Commons Speaker was forced to apologise after chaotic scenes in parliament.
The move marks a change in the party's long-standing position on the conflict.
MP will this week vote on the party's motion demanding an immediate end to the violence.
The move is designed to head off a rebellion by shadow ministers who back a ceasefire in the conflict.
Scotland's former first minister was mobbed by reporters and supporters at the party's annual gathering.
The party has agreed on yet another new policy on how to break up the United Kingdom.