Madrid are enjoying a good second season under Jose Mourinho as they currently top La Liga by three points ahead of Barca and have also been impressive in European competitions as well.
However, Madrid continue to struggle in head-to-head clashes against the Catalans as highlighted by their 3-1 defeat in El Clasico at home earlier this month.
Pedro warns Madrid must not be underestimated, especially as a potential meeting with Mourinho's team is on the cards in the Copa del Rey quarterfinals.
"Yes, it is possible to cross with Real Madrid, but let's go step-by-step," Pedro told AS.
"They are very strong physically, they are a tough opponent."
Barcelona romped into the last 16 of the Copa del Rey with a 9-0 victory over minnows Hospitalet at the Nou Camp.
"I'm happy about the last game, but you have to think about the next, which will also be complicated," Pedro said.
"We know that the road is long and difficult, but we can do it calmly."
The competition's fifth-round draw pitted reigning champions Madrid against Malaga, while last year's beaten finalists Barca will play Osasuna.
The two bitter rivals could then meet each other in the quarterfinals should they win both their fifth-round ties.