The former Liverpool defender believes the Spaniard has risked not being remembered by fans.
The former Reds defender believes the Spaniard has risked not being remembered by fans of his new club due to his previous allegiance to Arsenal.
And, at the same time, Carragher fears the good memories of Fabregas's time with the Gunners may be wiped from Arsenal supporters' memories.
Owen moved to Manchester United in 2009 after previously being seen as a Liverpool idol and the 36-year-old sees comparisons between his and Fabregas's current situation.
"I can understand why some players make certain moves - to be fair to Cesc, he didn’t have many top options this summer and Arsenal didn’t want him back - but, equally, I can’t understand why some jeopardise something they have worked hard to build up for a couple of years with the enemy," Carragher wrote in the Daily Mail.
"Look at the example of Michael Owen. He should be idolised on The Kop after the goals he scored for Liverpool - but his subsequent spell with Manchester United means he will never be afforded the same affection as Robbie Fowler or Steven Gerrard. United fans are just as indifferent to him."
Fabregas, 27 has already made an impact on-field for the Blues, registering two assists in their Premier League opener at Burnley, where Jose Mourinho's men won 3-1 to take them to the league summit based on goals scored.
Chelsea face Leicester City next on Saturday afternoon, before travelling to Everton the following weekend.