Mr Erdogan announced the move after links to recordings that appear to incriminate him and other top officials in corruption appeared on the site.
Turkey has previously blocked access to YouTube, but it is the first ban on Twitter, which is hugely popular in the country and was instrumental in organising flash protests against the government last year. Uproar over the recordings has damaged the government's reputation ahead of local elections this month.
Despite the ban, tech-savvy users managed to tweet links to the recordings.
Many users trying to access the network yesterday saw a notice from Turkey's telecommunications authority, citing four court orders.
Turkey's lawyers' association asked a court to overturn the ban, arguing it was unconstitutional and violated Turkish and European human rights laws. Turkey's main opposition party also said it would seek a cancellation.
European Commission vice president Neelie Kroes criticised the Twitter ban as "groundless, pointless, cowardly".
The ban comes amid reports that even more damaging recordings are about to emerge.