On the one hand there are some Muslims (and Christians and Jews) who view Yoga as problematic, especially because its more ritual elements (like chanting) arguably constitute the practices of another religion. On the other hand there are Muslims (and Christians and Jews) who either replace the ritual elements with content from their own faiths, or eliminate the chanting altogether and emphasize the physical aspects of yoga (stretching, asanas, breathing).
Malaysia clerics issue yoga fatwa
Indonesian clerics ban Muslims from practising yoga
Deoband intervenes: Muslims can do yoga
At least one Muslim (for example the author of the article Islam and Yoga) goes even further and argues that while syncretism between Islam and Yoga is "spiritually invalid", nevertheless there are many correspondence between Islam and Yoga beneath the surface.
On yet another hand (after all, we are discussing Indian religion) recently the Hindu American Foundation is concerned with the way in which some practitioners of Yoga seen to have divorced Yoga from its Hindu roots and so they have launched a "Take Yoga Back" campaign. (see the article: Is Yoga Hindu?) The article reminds me of similar questions about the way Sufism (or these days Rumi's poetry) is sometimes divorced from Islam.
And on yet another hand, the last point is reminiscent of questions of cultural appropriation which we have discussed before in white people and native religion.
The moral here is tricky I think. To the extent that Yoga is just a form of physical exercise with certain heath benefits it is acceptable to Muslims (and Chrsitans and Jews). But the more Yoga is connected integrally to Hinduism, the less acceptable it is for non-Hindus to follow. And to the extent that Yoga is a cultural practice of a specific group of people, we should be aware of its history.