I've heard opposite opinions on this (for example, in an interview with Christine Mangala Frost) and I was wondering about it.
So is Eastern Orthodox Christianity against doing yoga or meditation?
I don't think there is any council-wide declaration about this, but most of the clergy will advise against such practices. To see why, we need to look into the traditional orthodox spirituality (hesychasm).
The Holy Fathers put a complete and definitive set of spiritual practices which include fasting, remembrance of death, remembrance of own sins, Jesus' prayer, reciting psalms, prostrations, sitting during some prayers, standing during others etc.
Orthodox Christianity strongly states that there is a strong bound between orthodoxy (correct faith) and orthopraxy (correct practices). As shown during the hesychast controversy these practices are really important and their results are not merely physical.
With this looking for the school of meditation and psycho-physical practices outside the orthodox tradition; from religious and spiritual traditions that have different than Christianity views on human salvation is unjustified.
Yes, Eastern Orthodox Christianity is against doing Yoga, meditation and whatever else 'new age' practisisms. Those practisisms are NOT Orthodox.
Please read this article. It talks about the incompatibility of Yoga And Orthodox Christianity. It is written by Father Charles Joiner of the Saint George Greek Orthodox Cathedral in Greenville, South Carolina.
P.S.: I'm Greek Orthodox.