There are two challenges in answering your question. First, art is subjective, so there is much disagreement over what may be considered artistic. Second, preservation is both nature's blessing and curse to archaeologists. Much of the intentionally created work people have produced throughout history has been destroyed by moisture, light, bacteria, and aging. The best-preserved examples of ancient art that we have are either entirely or partially made of stone. We have certainly lost much more wood, fiber, and plant material art that can never be accounted for in the archaeological record. There may even have been works of art much older than the ones I am about to describe that simply did not survive to be known to our time.
Anthropologists, including archaeologists, generally define art as something not solely useful (though useful items may be made beautiful with art) that has been created or transformed with human intention. After that, beliefs about beauty, design, and form really complicate things. For our purposes, let's work with the understanding that a piece of art is anything that has been made more attractive or interesting to humans for the sake of enjoyment.
The earliest stone tools date to around 2.6 million years ago, and after a while, our ancestors realized that, in addition to helping them prepare food, tools could also make beautiful things. Several species who lived before us (Homo sapiens) created art, including Homo erectus. The absolutely oldest evidence of intentionally-altered material are the cupules carved into cave walls in places like Bhimbetka, India. These round, pock-like marks in cave walls would have been created by Homo erectus who spent time sheltering in such caves as early as 700,000 years ago. Of course, we don't know if they considered these anything spectacular or artistic — they might have just been bored and had a rock on hand.
Much later, around 100,000 years ago, the first beads (which remain preserved to this day) were created. At Skhul cave in Israel, perforated shells have been found alongside human remains. By this time, our own species was on the scene and getting creative, but members of the species Homo sapiens did not begin to migrate out of Africa until at least 70,000 years ago. For that reason, these shells were most likely poked and strung by Homo neandertalensis. Similar beads have been found in Morocco, dating to around 82,000 years ago, and may have been made by members of our own species.
The oldest examples of intentional artwork made by Homo sapiens, our own species, come from Blombos Cave in South Africa. Here, around 100,000 years ago, humans were making decorative stone and bone tools and paints. Pieces of carved ochre, a rich red or yellow pigment, have been here and date to around 76,000 years ago. It has been suggested that this means of carving regular patterns into the ochre was for keeping track of information rather than decoration. If we accept this hypothesis, we can move on to the next oldest example of intentional manipulation of materials. At Diepkloof, also in South Africa, engraved ostrich eggshells have been found dating to around 60,000 years ago.