On Tuesday, the company's shares led gains on the Hong Kong bourse and it was the third most actively traded stock. At one point, it was up 668.6% on the day before retreating slightly. Since Friday's close, Next Digital has risen 2,078%.
"Investors are strongly advised to exercise extreme caution," the Securities and Futures Commission said in a statement after Tuesday's market close. It said it had been monitoring and would continue to monitor the shares.
Police on Monday detained Lai, along with other executives of his media company in the highest-profile arrest under a national security law imposed by Beijing, which critics say crushes freedoms in Hong Kong.
Pro-democracy activists have started a campaign to encourage buyers for Next Digital shares and for the Apple Daily anti-government tabloid it publishes.
More than half a million copies of the paper were published on Tuesday, up from the usual 100,000. Buyers queued in the early hours and vendors had to re-order issues before the morning commute time.
One post on a local forum used by pro-democracy supporters said: "Freedom is priceless, use $$ to support Jimmy Lai."
Next Digital's market value has risen from HK$197.7 million ($25.42 million) early on Monday to HK$5.17 billion ($666.71 million).
The media group said in a bourse filing its operations have continued normally and it did not expect the arrests to impact its financial position.
Brokers said the surge was also driven by speculation Lai may sell the business.
"Speculation of sale of control and its low price level provided day traders a convenient excuse to bet on the stock," a strategist from a local brokerage said, asking not to be named.
Another local media stock, Most Kwai Chung Ltd has also jumped 292% so far this week.
Most Kwai Chung's board said in a filing it was not aware of any reason for the price increase.
($1 = 7.7500 Hong Kong dollars)
(Reporting by Donny Kwok and Clare Jim; Additional reporting by Alun John; Editing by Barbara Lewis)