Some scientists say that for every particle there exist an anti-particle. If this is true, does it mean that there would be an anti-particle for the Higgs boson also? Could it be that the massless particles would interact with this anti-particle for the Higgs boson?
Your first statement is true. However, there is a subtlety - some particles are their own antiparticles.
My understanding is that antiparticles are one particle states (irreducible representations in quantum state space of the Poincaré group see my answer here of what this means) that are mapped into one another by the CPT operator (or better written $C\circ P\circ T$) - time reversal followed by parity inversion followed by charge conjugation.
Some such one particle states are invariant under the action of the CPT operator. It follows by the above definition then that such particles are their own antiparticles. The Higgs Boson is one such particle.
"Antiparticle" and "particle" are partly just words and definitions. Essentially we say that a particle is its own antiparticle if it can emerge alone (i.e. not belonging to a pair) from any quantum state with the requisite momentum, energy and angular momentum. There are no other quantities, such as electric charge, which need to be conserved and therefore pairs of opposite charges or the like are not needed to conserve such quantities.