Shares rose 3.7 percent on Thursday but were trading down Friday after the disclosure on the FTC's website on Wednesday.
The approval allows Appaloosa to acquire more shares of Allergan, in which it already has a 1 percent stake of 3.7 million shares, according to FactSet's count. Allergan's shares are down nearly 27 percent over the last 12 months.
Investors who want to take an activist stance by engaging with company management have to abide by FTC rules that require approval for anyone taking a stake greater than $84 million. At $593 million, Appaloosa is already well past that threshold, but the approval gives it flexibility if it decides it wants to become more than a passive investor.
Tepper's Appaloosa has been making changes to its holdings, disclosing earlier this week it exited a 4.6 million share stake in Apple and a 1.98 million share stake in Comcast and added new stakes in Applied Materials and Wells Fargo. It started building its Allergan stake in 2015.
Tepper is also in a $2.2 billion deal to buy the Carolina Panthers professional football team.
A spokesman for Appaloosa said he had no comment on the Allergan approval.
Allergan, the maker of Botox and Juvederm, began a strategic review of its business earlier this year, including possible sales of business units or a splitting up of the company.
CEO Brent Saunders said on a conference call in April, "While the board continues to evaluate the options, my preliminary view is that a fundamental shift in the overall business strategy is not necessary."
A spokeswoman for Allergan said the company "welcomes all investments in our company."