Left-wing website sendika.org said its editor-in-chief Ali Ergin Demirhan was held in a pre-down raid on its offices.
The arrest comes after at least 16 leftist activists involved in demonstrations against the 'Yes' victory were detained by Istanbul police on Wednesday. In all, a total of 38 arrest warrants were issued.
The 'Yes' camp won Sunday's poll with just 51.41 percent of the vote but the opposition has alleged there was foul play that swung the outcome of the vote.
The authorities insist the referendum was clean and the election board on Wednesday rejected opposition demands for the poll to be annulled.
There have been daily street protests in anti-Erdogan neighbourhoods in Istanbul after the referendum.
It added that his hard disk and personal cell phone were confiscated in the raid.
The news site has made clear its opposition to the result, saying "the 'Yes' will not be legitimised, sendika.org will not be silenced" and calling for protests.
The opposition is particularly incensed by a last-minute move by the election authorities to accept ballot documents in envelopes without an official stamp.
Turkish media said that six people were detained in the Aegean city of Izmir on accusations of "insulting" Mr Erdogan in public on the night of the referendum.