Is reduction of copper oxide a combustion reaction?
By the question asked, I assume OP is in high school of freshman in college. Thus, I'd use this general description of combustion as a starting point: 


  Combustion reactions are common and very important. Combustion means burning, usually in oxygen but sometimes with other oxidants such as fluorine. A combustion reaction happens quickly, producing heat, and usually light and fire. Combustion describes how the reaction happens, not the reactants and products. Chemists as early as Lavoisier suggested that people get their energy from combustion-like reactions, but even though the products and reactants are the same when you burn food in a fire and in your body, the way it happens is different. In a combustion reaction, the thing that burns (the reactant that isn't $\ce{O2}$ or $\ce{F2}$) is called the fuel. Combustion reactions are a type of redox reaction.


As  M. Farooq pointed out a combustion reaction happens quickly, producing heat, and usually light and fire. For example, lets look at combustion reaction of an alkene (a hydrocarbon). If it is a complete combustion, the fire have a blue flame:

$$\ce{C_nH_{2n} + $\frac{3n}{2}$ O2 -&gt; nCO2 + n H2O}$$

If it is a partial combustion, it can have a multiple $\ce{C}$ compounds as products, and have a yellow flame due to presence of elemental $\ce{C}$:

$$\ce{C_nH_{2n} + x O2 -&gt; m C + p CO + $(n-m-p)$CO2 + n H2O}$$

where $x = \frac{2(n-p-m) +p}{2} = \frac{2n-2p-2m +p}{2} = \frac{2n-p-2m)}{2}$. In your reaction would not produce fire and it didn't use either oxygen or other oxidants ($\ce{CuO}$ is not that type of oxidant). It is true that the reaction is a redox reaction.