NO, it's unsubstantiated.
While I can't definitively debunk it, because no experiments were made, or published that debunk this claim, there were also no supporting scientific publications, neither experiments nor theoretical. There is simply no scientific background for this.
It's all based on Solfeggio frequencies:
[Solfeggio frequencies] referring to a belief that a set of nine frequencies derived from numerology were used centuries ago in Gregorian and Sanskrit chants
first introduced in a 1999 book published by a person* who also claimed:
AIDS and Ebola were engineered by the U.S. government with biological warfare and genocide in mind.
In his self published book Emerging Viruses: AIDS and Ebola: Nature, Accident, or Intentional?
It's based on speculation and Numerology, non of which is a scientific proven theory. The specific numbers for the frequencies are derived by some strange and unexplained numerologic calculation:
The numerical values of the Solfeggio Frequences are generated by starting with the vector (1, 7, 4) and adding the vector (1, 1, 1) MOD (9). Each higher frequency is found by adding (1, 1, 1) MOD (9) to the previous lower frequency. The final frequency, when (1, 1, 1) is added to is, returns the frequency to the lowest tone (1, 7, 4).
Ut = 396 Hz which reduces to 9 [reducing numbers: 3+9 = 12 = 1 + 2 = 3 ; 3+ 6 = 9]
Re = 417 Hz which reduces to 3
Mi = 528 Hz which reduces to 6
Fa = 639 Hz which reduces to 9
Sol = 741 Hz which reduces to 3
La = 852 Hz which reduces to 6
* - It should be noted that the author is a dentist and has published some articles regarding Dental Health ( "Horowitz LG" (Author) – PubMed Results), But he has no formal training, published papers or published research on DNA, DNA repair or any other related topic.
Vibrations within the hearing range or close to it might help humans heal (research in the area is not conclusive), but it's in different frequencies and with different illnesses, some examples:
Whole-body vibration to treat low back pain: fact or fad?
Acute exercise with whole-body vibration decreases wave reflection and leg arterial stiffness
The effect of whole body vibration exposure on muscle function in children with cystic fibrosis: a pilot efficacy trial.
Transmissibility of 15-hertz to 35-hertz vibrations to the human hip and lumbar spine: determining the physiologic feasibility of delivering low-level anabolic mechanical stimuli to skeletal regions at greatest risk of fracture because of osteoporosis.