Thor's hammer, Mjolnir cannot by itself, destroy Captain America's shield. It cannot even dent Captain America's shield.
Mjolnir is a magical weapon, imbued with incredible physical and magical properties but none of those powers can destroy Adamantium. Thor for all of his physical might has never managed to do anything to Cap's shield until the introduction of the Odinforce to Thor's arsenal.
Despite Mjolnir's pedigree, forged of uru metal by Dwarven blacksmiths with the energy of a star, and having almost no equals in Asgard, save the Spear of Odin, Gungnir. Captain America's shield is composed of Proto Admantium (a never duplicated variant of vibranium and true adamantium) has resisted attacks from Thor's hammer (and almost anything else the Marvel Earth-616 has thrown at it) for most of the career of the two characters.
On Marvel Earth-616, Captain America's shield has been broken 6 times in its history (Marvel makes sure anytime Cap's shield has been broken by less than extraordinary means, those instances were retconned out by "replicas.") In all circumstances where the actual shield was destroyed, it was by beings whose powers exceeded mere physical strength and was coupled with extreme levels of sorcery-enhanced might, energy manipulation, or reality alteration.
Destruction of the shield
As of 2011, Wikipedia lists that the the shield has been damaged or destroyed several times within the confines of the Earth-616 continuity. On each of these occasions, the shield was subjected to a cosmically powerful force capable of reshaping matter on a massive scale. Specifically, the powers that affected the shield are:
- In The Avengers #215–216, the Molecule Man used his total control over matter to disintegrate the shield, along with Thor's hammer, Iron
Man's armor, and the Silver Surfer's board. After he does so, he
comments that the board's molecules are "weird", and while there are
"odd forces interweaving" among the hammer's molecules, the shield is
"weirdest of all". He later reassembles these items, with the
exception of the armor, as the electronic circuits are too complicated
for him to understand.
- During the 1984-1985 Secret Wars limited series, the shield is partially destroyed by Doctor Doom, who has stolen the power of the
godlike being known as the Beyonder. Even broken, Rogers is able to
wield what is left as an effective weapon, with the shield largely
retaining its balance when thrown. When the Beyonder reclaims its
power, the heroes are temporarily granted the ability to realize their
wishes. Rogers uses this to reconstruct the shield. It later shatters
into dozens of pieces, due to a sub-molecular imperfection introduced
into the vibranium. Rogers has the pieces taped back together, and
during a battle with the villain Klaw, Klaw's shock wave–augmented
power realigns the shield's vibranium molecules and restores the
- During the 1991 miniseries The Infinity Gauntlet, Thanos, who possesses near-omnipotence via the Infinity Gauntlet, shatters the
shield with a blow of his fist while in combat with Captain America.
The shield is soon restored by Thanos' alleged granddaughter, Nebula,
when she obtains the Gauntlet and uses it to undo the events of
Thanos's temporary godhood, resulting in her erasing the death and
destruction that Thanos had caused over the previous 24 hours.
- In Avengers Vol. 3 #63 (March 2003), the Odinforce, wielded by an enraged Thor, dents the shield. Thor later repairs it.
- In "Thor" Vol. 2 #73 (January 2004), the Odinforce, again wielded by an enraged Thor, destroyed the shield, killing Steve Rogers with
it. This timeline was later erased in "Thor" Vol. 2 #79.
- During the 2011 miniseries Fear Itself, the Serpent, the Asgardian god of fear and brother to Odin, breaks it in half with his bare
hands. After the battle, the shield is repaired by Asgardian dwarves
with added Asgardian uru-infused enhancements to make it stronger,
though a noticeable scar on the surface is visible, which Captain
America elects to keep to give character to the shield.
It is the Odinforce that allows Thor to dent and later destroy the shield of Captain America. The Odinforce is amazingly powerful and with it, Thor was exponentially more powerful than he was without it, literally the equal of Odin, who should be able to destroy the shield with sufficient expenditure of molecular manipulation.
...the Odinforce - a powerful source of energy - for a number of
purposes, including energy projection; creation of illusions and force
fields; levitation; molecular manipulation, communicating
telepathically with other Asgardians even if they be on Earth and he
in Asgard, hypnotizing humans; channelling lightning to
Earth from Asgard, controlling the lifeforces of all Asgardians,