The midfielder was shown the red card after appearing to kick the youngster for holding onto the ball too long in the League Cup semi-final second leg.
"South Wales Police are investigating an incident involving Eden Hazard and a ball boy following complaints," Sky Sports News posted on its Twitter account.
Both managers have pointed out that the ball boy should not have withheld the ball, but neither condoned the actions of Hazard.
"We can analyse if for half an hour but we know that both are wrong," Chelsea boss Rafael Benitez told BBC Sport.
Swansea's Michael Laudrup added: "The ball boy should have let the ball go but he was pushed first and then he kicks him.
"As a player when you are behind your pulse is very high and sometimes you say and do things, you overreact. But there are some things you cannot do."
The game finished in a 0-0 draw, meaning that Swansea progress 2-0 on aggregate to set up a final against League Two Bradford City.