Before his omission was confirmed by the club, Ghana international Williams had not missed a league game since the 2015-2016 season.
The 28-year-old was suffering an unspecified physical problem that meant head coach Ernesto Valverde had to cope without the team's mainstay.
Williams surpassed the previous record of 202 consecutive games when he featured in the win over Alaves in October 2021, going past the mark set by former Real Sociedad stalwart Jon Andoni Larranaga.
The marathon ever-present spell began for Williams on April 20, 2016, when he appeared as a substitute in a 1-0 defeat against Atletico Madrid.
During the 251 games, Williams scored 50 goals and had 31 assists, from totals of 456 shots and 207 chances created.
Athletic won 89 of those games, losing 84 and drawing 78.
Since Williams' run of games began, up to and including Sunday, Atletico goalkeeper Jan Oblak made the second-most appearances in LaLiga, featuring in 240 games.
Williams started 212 matches and appeared as a substitute 39 times across his marathon stint for Athletic.