Jonathan Edwards did not vote on a motion expressing confidence in the Government in the House of Commons on Monday.
Unusually, the vote was tabled by the Government because it refused to accept the wording of a Labour motion after Boris Johnson announced he was staying on as Prime Minister until the autumn.
MPs were asked whether "this House has confidence in Her Majesty's government", with defeat almost certainly triggering a general election.
The Independent MP for Carmarthen East and Dinefwr did not register a vote on the motion which passed 349-238.
Voting for the motion were 342 Tory MPS, six DUP MPS and one Independent MP.
Meanwhile, 181 Labour MPS, 37 SNP MPS, 12 Lib Dem MPS, two Independent MPS, one SDLP MP, one Alliance MP, three Plaid Cymru MPS and one Green Party MP voted against it.
There were just 48 who abstained or did not vote – 16 Labour MPS, 12 Tory MPS, seven SNP MPS, two DUP MPS, six Independent MPS, one SDLP MP, two Alba Party MPS and two Lib Dem MPS.
The vote counts do not include the four MPs who acted as tellers, the seven Sinn Féin MPs who do not take their seats, the Speaker or the three Deputy Speakers.