A scan on Monday showed he had damaged his ankle ligaments and it was "almost certain" de Boer would not play again at the tournament, the Dutch said in a statement.
De Boer, 34, has won a Dutch record of 112 caps and had said he would retire after the tournament. He did not train with the rest of the squad on Monday.
De Boer was substituted during the first half of Saturday's quarter-final win over Sweden after hurting himself in a tackle on Swedish midfielder Fredrik Ljungberg.
He did not play in the first two group matches against Germany and the Czech Republic but replaced the injured Wilfred Bouma in the starting lineup for the third game against Latvia.