Is the shape of observable universe and shape of space same? I have read that Euclidean space is considered as flat space and Minkowski space is flat space-time. So when we say our observable universe is flat are we saying that the space is flat or space-time is flat? I know the Planck data has proved the space to be flat but is it only space or space-time? Since in general relativity matter curves space-time and not just space.
When talking about curvature in (General) Relativity one usually refers to the metric interval and how this depends on the space-time coordinates.

For example, the metric interval in Minkowski space can be written
$$ ds^2 = c^2\ dt^2 - dr^2$$

This is an example of both flat space and flat space-time. It is flat space because if I want to find the distance between two events happening at the same time $t$, it is simply the integral of $dr$.

Similarly I can ask what the time interval is between two events and this is just given by the integral of $dt$.

A counterexample is seen when using the Schwarzschild metric, which is appropriate in the space outside a spherically symmetric mass. Considering only the radial and time components, the metric is
$$ds^2 = c^2 (1 - r_s/r)\ dt^2 - (1- r_s/r)^{-1}\ dr^2,$$
where $r_s = 2GM/c^2$ is the Schwarzschild radius associated with the mass $M$.

Now there is no simple relationship between $dr$ and the spatial separation between two events that occur at the same $t$, we must do an integral. Similarly, to work out the time interval between two events at the same $r$ we must do a more complicated integral. Both space and space-time are curved.

The evolution of the universe as a whole is governed by the Robertson-Walker metric.
$$ds^2 = c^2\ dt^2 - a(t)^2\frac{dr^2}{1 - kr^2},$$
where $k$ is a curvature parameter that may be -1, +1 or zero.

At the moment, the best measurements are consistent with a zero curvature - that the universe is spatially flat. That does not mean it is flat on much large scales than we can observe - that is still possible. A curved universe that was exponentially "inflated" shortly after the big bang may well mimic a flat universe even though the curvature is finite.

Note though that because the universe is inherently "lumpy", this spatial flatness is only true on scales much larger than planets, stars, galaxies and even clusters of galaxies.

Whether you could call space-time flat in a spatially flat Robertson-Walker universe I doubt. The reason for this is the time-dependent scale factor $a(t)$, which ensures there is a coupling between the $r$ and $t$ coordinates. It is this coupling that is responsible, for example, for the cosmological redshift of light. 

A technical answer would need to look at the Einstein Tensor which characterises the curvature of space-time caused by mass and energy. In the Robertson-Walker metric, this tensor definitely has non-zero components, so you would have to say that even if space is flat, space-time is curved.