The Scotland international was in line to start against the Hammers, but was pulled out at the last minute due to ‘muscular discomfort’ and replaced by Sead Kolasinac.
Tierney’s strong presence in defence and attack was missed as the Gunners struggled to a narrow victory against David Moyes’ side.
Arsenal struggled to get any passing rhythm going and took the lead against the run of play in the first half, with Pierre-Emerick Aubameyang setting up Alexandre Lacazette for a simple header.
West Ham clawed a goal back through Michail Antonio on the stroke of half-time as they were rewarded for their tenacious display.
Despite the Hammers having the better opportunities in the second half, a smart pass from Bukayo Saka set Dani Ceballos free, who squared it for Eddie Nketiah to roll into an empty net late on, handing Arteta’s side their second successive win in the Premier League.
He said: ‘Kieran is fine. He had a little muscular discomfort in the last few days. He tried today and worked in the warm-up but he wasn’t feeling comfortable today.
‘We could not control it. We believed that he was going to be fit but during the warm-up, in the last 10 minutes, he said he wasn’t feeling OK.
‘We had to make a decision. We were prepared just in case and Kola came on and had a good game.’