2013 will see Button's fourth season at McLaren and the first year that Lewis Hamilton will not be his teammate.
Horner has insisted that those who are underestimating Button will be surprised.
"Probably to everybody's surprise Jenson went to what was perceived as Lewis's team and gave them something to think about," Horner told the The Guardian.
"He morphed the team around him and it will be interesting to see [what happens] this year as he is very much the de facto team leader.
"If the car suits his requirements then there is no reason why [he can't challenge for the title this year]. He is certainly a driver that we do not underestimate."
The 2013 Formula 1 season begins in Australia on the weekend of March 15-17.