Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Changing the genes in the cell of a plant, animal or human is allowed if it is for a good purpose, such as treating a hereditary disease.
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
Changing the genes in the cell of a plant, animal or human is allowed if it is for a good purpose, such as treating a hereditary disease. However, modifying genetic material for purposes of eugenics or to produce hybrid organisms for entertainment/curiosity is prohibited.
There is a potential unknown long-term harm associated with such modification that could affect the environment, crops, animals, and humans and therefore all genetically modified organisms should be labeled as such so that people know what they are buying.
Almighty Allah knows best.
Source: AsktheScholars.com