People have “surged” to join Nicola Sturgeon’s party, a source said, to unite against a “power grab” by the Conservatives on Brexit.
They added the normal comparable figure is 50-100, making the daily growth up to nearly 10,000% higher than usual.
SNP MPs stormed out of the Commons chamber when their Westminster leader Ian Blackford was kicked out by the speaker during PMQs.
He was protesting at MPs being given around an hour to consider over 50 amendments to the Brexit bill on devolution.
An SNP insider credited the membership boom on “Tory attacks on devolution”.
They told Sky News: “Scotland will not be silenced and voters are uniting against the brazen Tory power grab.
“Like the party’s extraordinary membership surge of 2014, joining the SNP has become a powerful symbol and the best way of ensuring Scotland’s voice is heard.”
Downing Street on Wednesday dismissed as a “stunt” the disruption of Theresa May’s weekly grilling in Westminster.
The prime minister’s spokesman said: “That sort of stunt effectively means that the SNP members who were down on the order paper to ask the PM questions can’t represent their constituents.”
Scotland Secretary David Mundell also said: “The SNP was about to be granted a debate on how the devolution aspects of the EU Withdrawal Bill.
“Disappointed, if not surprised, that if they really felt so strongly about it, they chose a stunt over holding the Government to account.”