Monitor said the probe into the Christie NHS Foundation Trust was over concerns about governance and was not over allegations relating to suspended chief executive Caroline Shaw.
Chairman Lord Bradley announced he was resigning from the trust on Friday.
The Christie Hospital said in a statement: "There will be no further comment or interviews."
Monitor said it was examining whether the trust had breached its licence to provide healthcare services by failing "the principles of good governance".
It said there were concerns the board of the trust had "not adhered to the required corporate governance standards".
John Leech, Liberal Democrat MP for Manchester Withington, described the management situation at the hospital as "a mess" following Lord Bradley's resignation.
Lord Bradley said he would leave the trust as soon as a replacement could be found.
Ms Shaw was suspended in November as part of a disciplinary investigation.
Monitor said it will announce the outcome of its regulatory investigation "in due course".
The Christie in Withington said it is the largest cancer centre in Europe and treats more than 40,000 patients a year.
A cancer treatment hospital in Greater Manchester is being investigated by the health regulator.