Videos posted on YouTube appears to show Wenger, 65, being jeered and sworn at by fans as he boarded his train following his side's defeat at the Britannia Stadium that has left them sixth in the table 13 points behind leaders Chelsea.
One fan can also be heard yelling at striker Joel Campbell, walking just ahead of Wenger, "Get out while you can Joel."
Lineker, the former Spurs striker who is now a BBC Sport presenter, tweeted: "Just saw the Wenger abuse video.
"Disgustingly disrespectful and totally inexcusable, regardless of any football results" he said.
Wenger was also the target of criticism from Arsenal fans during his side's 1-0 win at West Bromwich Albion last weekend where some Arsenal fans unveiled a banner that read: "Arsene, thanks for the memories but it's time to say goodbye."
A fight also broke out between Arsenal fans who support Wenger and those who want to see him leave after the match at Stoke according to a report in the Sun on Sunday.
One fan tweeted: "Fist fights between Arsenal fans after the game, absolute joke. Disgusting to see our own fans punching each other."
Wenger remained in the dugout throughout the game so that Stoke fans, angered by him saying in the past that they were a "rugby team", could not see him.
"I didn't want to give them an opportunity to show me their love," he said afterwards.
Wenger has been Arsenal manager since 1996 and ended a wait of nine years without a trophy when the Gunners beat Hull City to win the FA Cup in May.
(Reporting by Mike Collett, editing by Alan Baldwin)
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