Carragher's spittle is believed to have hit the driver's 14-year-old daughter, and since the footage came to light, the 40-year-old has issued an apology.
Lineker, who anchors BBC's Match of the Day, initially poked fun at the incident on Twitter by saying: "Seems @Carra23 can't do it on a cold, damp Monday night at Stoke."
The former England international was referencing the fact that Carragher was absent from his punditry duties for Sky's coverage of the Premier League clash between Stoke City and Manchester City.
Lineker then added: "On a serious note, we all make mistakes, @Carra23 made a big one. He's apologised and is clearly contrite. Sure he'll be back soon and rightly so."