This paper investigates the mechanical properties and creep behavior of undoped and Mg-doped GaN thin films grown on sapphire substrates using metal–organic chemical vapor deposition (MOCVD) with trimethylgallium (TMG) and bis(cyclopentadienyl)magnesium (Cp2Mg) as the precursors for Ga and Mg, respectively. The Mg-doped GaN layer, with a [Mg]/[TMG] ratio of 0.33, was systematically analyzed to compare its mechanical properties and creep behavior to those of the undoped GaN thin film, marking the first investigation into the creep behavior of both GaN and Mg-doped GaN thin films. The results show that the incorporated [Mg]/[TMG] ratio was sufficient for the transition from n-type to p-type conductivity with higher hole concentration around 4.6×1017 cm−3. Additionally, it was observed that Mg doping impacted the hardness and Young’s modulus, leading to an approximately 20% increase in these mechanical properties. The creep exponent is also affected due to the introduction of Mg atoms. This, in turn, contributes to an increase in pre-existing dislocation density from 2 × 108 cm−2 for undoped GaN to 5 × 109 cm−2 for the Mg-doped GaN layer. The assessment of the creep behavior of GaN and Mg-doped GaN thin films reveals an inherent creep mechanism governed by dislocation glides and climbs, highlighting the significance of Mg doping concentration in GaN thin films and its potential impact on various technological applications.