Fox has also offered to buy the 61% stake in Sky it doesn't already own for a total of GBP11.7 billion, or GBP10.75 a share.
While Fox's Sky deal awaits approval, Disney made a separate bid to buy most of Fox back in December, including its existing stake in Sky.
"Sky notes the ruling announced by the panel executive, earlier today, that The Walt Disney Company will be required to make a mandatory offer for Sky at a fixed price of £10.75 in cash per Sky share within 28 days of completion of Disney's proposed acquisition of Twenty-First Century Fox, unless by then 21st Century Fox has acquired 100 percent of the Sky shares, or any third party has acquired more than 50 percent of the Sky shares", Sky said.
If Comcast ends up acquiring Sky, Disney would not have to put forward a bid, the Takeover Panel said.
Meanwhile, a year ago Disney agreed to buy Fox's entertainment assets including its stake in Sky, in a separate deal which is also subject to regulatory clearance.
Sky shares were mostly unchanged at 1,311 pence in London on Thursday morning.
"21CF remains committed to its recommended cash offer for Sky announced on 15th December 2016, which is supported by revised remedies recently offered to the Competition and Markets Authority (CMA) with whom 21CF has been co-operating in order to bring the United Kingdom regulatory process to a swift and satisfactory conclusion", Fox said in a statement.
Although the deal was approved by European authorities, it was derailed by Britain's competition watchdog, who said in January that it is not in the public interest as it would give the global media mogul Rupert Murdoch and his family "too much control" over the country's media.
The three companies - Sky, Fox and Disney - signed a confidentiality agreement in March.
Sky separately said that shareholders should not take any action, and further advice will be announced in due course. However, Fox has proposed remedies to allay the regulators' concerns.
"We think Sky is an outstanding company", said Comcast CEO Brian Roberts in a statement at the time.
Meanwhile, it is awaiting the outcome of the United Kingdom competition regulator's verdict on whether to allow Murdoch to buy the 61% of Sky he does not already own - a deal that was well in train before the Disney transaction.