On eve of an EU summit in Brussels, May told parliament that she has written to EU President Donald Tusk to ask for the withdrawal date to be moved from March 29.
The European Commission warned in an internal briefing note that delaying Brexit to June 30 would bring "serious legal and political risks".
The EU's executive arm instead urged leaders to choose instead a short delay to May 23 or a longer one at least until the end of this year.
At around 1300 GMT, sterling was down almost one percent in value, sliding to $1.3149, while the euro rose to 86.40 pence. The unit was already in negative territory prior to May's announcement.
Analysts expressed doubt that the delay extension would allow May's Conservative government sufficient time to resolve the crisis.
"The pound's Wednesday only got worse after the confirmation that Theresa May is seeking a short delay from the EU, one that arguably does not give the government enough time to get through a sterling-positive Brexit deal," Spreadex analyst Connor Campbell told AFP.
"It appears that, despite the various votes highlighting MPs unwilling to leave the EU without a deal, that kind of disastrous exit is still very much on the table."
Rebecca O'Keeffe, analyst at online broker Interactive Investor, was similarly downbeat.
"A short delay is being perceived as the worst of all possible worlds for the UK and sterling," she told AFP.
"Rather than resolve the crisis, it suggests that Mrs May is likely to undergo three more months of brinkmanship.
"This will represent one more damaging quarter for UK businesses, especially those who had already implemented plans to cope with an end-March Brexit date.
"So it really is no surprise that the pound is going down, as investors face the prospect of another three months of purgatory."