Two news portals claimed last month that Shah ordered the illegal surveillance of a woman at the behest of a "saheb", widely believed to be Gujarat Chief Minister Narendra Modi.
The Gujarat government has already ordered a probe into the case. Shah is now in charge of Uttar Pradesh for the Bharatiya Janata Party.
The BJP reacted angrily to the decision, saying the real target was Modi, now the party's prime ministerial candidate.
"The Congress is trying to hit at the principal opposition party's prime ministerial candidate. It is a clear case of political vindictiveness coming into play," spokesman Nirmala Sitharamn said.
