The reason for Shenron's fear becomes evident when exploring the immense power of Beerus, the God of Destruction.

Shenron is the Earth Dragon God, appearing throughout the history of the Dragon Ball series. Renowned for wish-granting abilities, it plays a central role in many epic adventures.
Mighty as it may be, Shenron quivers in the presence of the God of Destruction, Beerus. So, what is the cause behind this fear?
How does Shenron perceive Beerus's strength?

Despite Shenron's extensive knowledge, it's not all-encompassing. Given Beerus's reputation and influence in Universe 7, Shenron has likely heard of this formidable God of Destruction. Dende, with a special connection to Shenron, also recognizes Beerus's divine might, indicating Shenron can sense the presence and power of the God of Destruction.
Why is Shenron afraid of Beerus?
When encountering Beerus, the dragon exhibits utmost humility and respect, revealing its fear. Shenron's behavior towards Beerus highlights the powerful and fearsome nature of the God of Destruction.

The reason for Shenron's fear becomes evident when examining the immense power of Beerus. As the God of Destruction, Beerus has the ability to destroy planets and potentially the entire Universe 7. He showcased his power in the battle against Super Saiyan God Goku, easily securing victory using only a fraction of his true strength.
On the other hand, Shenron and the Dragon Balls are not invincible and can be destroyed. If the creator of the Dragon Balls dies, the dragons will vanish permanently. Additionally, Shenron can be killed, as seen in the battle against King Piccolo, demonstrating that Shenron is not invulnerable.
Beerus, with his destructive power, can easily surpass Shenron in battle and annihilate both the Dragon Balls and their creator. This puts Shenron in an extremely vulnerable position against the God of Destruction.
Shenron vs. Beerus: Who is stronger?

Although Shenron possesses great strength, its power is limited by the strength of its creator. Shenron cannot harm someone more powerful than the one who created the Dragon Balls. Since Beerus surpasses Kami or Dende by a significant margin, he also outclasses Shenron in strength. This is evidenced by Shenron being defeated by King Piccolo, a villain much weaker than Beerus.
Beerus has the ability to defeat Goku in Super Saiyan God form, showcasing a level of power that Shenron simply cannot match. Therefore, Shenron knows it's best to maintain a respectful and cautious demeanor towards Beerus.