A bench of Chief Justice Dipankar Datta and Justice G S Kulkarni said this was an "extraordinary" and "unprecedented" case that warranted an independent inquiry.
In its 52-page judgement, the bench said Singh's allegations against Deshmukh had put at stake the citizen's faith in the state police.
Such allegations, made by a serving police officer, against the state home minister could not be left unattended, and were required to be probed into, if prima facie, they made a case of a cognisable offence, the HC said.
The court said a probe by an independent agency was necessary in the present case, to "instill public confidence and safeguard the Fundamental Rights of the citizens".
The HC pronounced its verdict on three public interest litigations (PILs) and a criminal writ petition filed last month, seeking several reliefs and a CBI probe into the matter.
One of the PILs was filed by Singh himself, and the other two were filed by lawyer Ghanshyam Upadhyay and local teacher Mohan Bhide.
The criminal writ petition was filed by city-based lawyer Jayshree Patil.
The HC ordered for the CBI inquiry on Patil's plea.
The court also disposed of all the pleas.
Singh, in his plea filed on March 25, sought a CBI probe against Deshmukh who, he claimed, had asked police officers, including suspended cop Sachin Waze, to extort Rs 100 crore from bars and restaurants.
Deshmukh has denied any wrongdoing.
The state's counsel, Advocate General Ashutosh Kumbhakoni, had urged the HC to dismiss all the pleas including that of Singh, saying they were not maintainable.
Kumbhakoni had said Singh filed the PIL to settle personal scores.
Besides, since no FIR had been registered in the case, a CBI inquiry could not be ordered, Kumbhakoni had said.
However, Jayshree Patil pointed out that she had registered a complaint against both Deshmukh and Singh at the Malabar Hill police station on March 21, but the police had failed to conduct a preliminary inquiry and register an FIR.
Noting the police's failure to conduct a preliminary inquiry based on Patil's complaint, even though the complaint showed cognisable offences had been committed, the bench said the court must intervene and grant relief.
The HC also said the nature of the allegations and the subsequent proceedings were unprecedented, and something that the two judges presiding over the pleas had never seen before.
"It is said that none can see time, but many a times, time makes us see many things hitherto before unseen. So true," the bench said.
"The proceedings of which we are seized lay bare incidents, allegations and approaches of a kind which, at least, the two of us have not experienced before," it said.
The court also took exception to the police's failure to act upon Patil's complaint.
"In fact, what the Constitution envisages is a rule of law and not rule of goons having political support," the court said.
The HC also said that all courts were committed to ensure the rule of law and to prevent any breach of constitutional principles, irrespective of however high an office an accused occupied.
The court said even though the state government had ordered for a high-level committee to probe into the allegations, an inquiry based on Patil's complaint was necessary as per the law.
Since the police investigating complaints against the home minister and a serving police officer would not be most appropriate, it is a fit case for ordering a CBI probe, the HC said.
It directed the CBI''s director to conduct a preliminary inquiry based on Patil's complaint and a letter written by Param Bir Singh to state Chief Minister Uddhav Thackeray that Patil had attached to her complaint.
The HC said the CBI need not immediately register an FIR, but it must complete its inquiry within 15 days and then decide on further course of action.
"It is indeed unheard of and unprecedented that a minister could be so openly accused of wrongdoings and corrupt practices by none other than a senior police officer," the HC said.
"This court cannot be a mere spectator in these circumstances. There is certainly a legitimate public expectation of a free, fair, honest and impartial inquiry. A probe into such allegations by an independent agency would also certainly be a requirement of the rule of law," it said.
After the HC verdict, Deshmukh resigned from the post of state home minister.