Inside the atmosphere, I guess the atmospheric pressure negates the pressure exerted by the gas that's inside a gas cylinder. However, when taken to a vacuum (space), Will the gas cylinder burst due to the pressure exerted on its internal walls by the gas that is present inside it?
The stresses in the wall of a gas cylinder can be estimated by modeling it as a thin-walked pressure vessel. The so-called hoop stress is $\Delta Pr/t$, where $\Delta P$ is the pressure difference, $r$ is the radius of the cylinder, and $t$ is the wall thickness. For a cylinder filled to a pressure of 100 bar, for example, the move from Earth’s surface (1 bar) to space (0 bar) would increase the stress by only 1%. As noted in the comments, the cylinder would have to already be at the threshold of failure for this increase to be important. Related scenarios can be considered for different values of pressure and factor of safety.