Vardy, who came on as a substitute in Saturday's 3-1 win, has now failed to score in his last 10 appearances for club and country.
John Stones tried to get one back on the other end, but Sergio Aguero's offside position cancelled out the goal.
English Premier League: Nathan Redmond (27') Manchester City 0-1 Southampton
English Premier League: Raheem Sterling (15') Manchester City 0-0 Southampton
Swansea chalked up a clean sheet for the first time in eight games, but there was a distinct lack of fire in the engine room.
If this was supposed to be a test of character after a 6-1 loss at Bournemouth seven days earlier, the Tigers failed it.