The 43-year-old was arrested by Police Scotland yesterday in relation to tweets directed at Mr Salmond and was detained in police custody.
He is expected to appear at Haddington Sheriff Court today.
The First Minister was informed of the arrest, it is understood, although there are no further details of the alleged abuse.
The move comes amid appeals from both the Yes and No camps for the final phase of the referendum campaign to be spared further vitriol as online attacks threaten to overshadow the independence debate.
A "cyberstorm" greeted the announcement by Harry Potter creator JK Rowling that she was donating £1 million to the pro-UK Better Together campaign.
A Police Scotland spokesman said: "We can confirm that a 43-year-old man has been arrested and is presently detained in police custody in connection with allegedly posting offensive tweets."