Engström called the decision "terrible", adding that the Swedish government is conducting a study into its assistance to the country, worth SEK 70 million in direct aid.
"I want to underline that our development assistance isn't unconditional. The Swedish government sees human and LGBT rights as an important condition", she told news agency TT.
The study will be completed this Spring.
Uganda receives around SEK 250 million in total from Sweden in development assistance each year, the rest going via the UN and NGOs.
Denmark has already announced it will transfer its direct aid to the country to NGOs as a result of the new law.