This question is probably best answered in two parts.
You may need to increase the ISO to combat noise. This sounds counter
intuitive due to common misconceptions regarding noise.
Noise is principally caused by lack of light. Lightsources emit photons randomly, the more photons you collect, the more the randomness averages out, leaving a smooth image. Fewer photons -> more random -> lots of grain.
All increasing the ISO does, is amplify the signal (and noise) you get from the sensor prior to digitization. It doesn't create noise, and as it amplifies the signal and noise by the same amount the signal to noise ratio remains the same. Needing to amplify the signal implies you have a weak (and hence noisy) signal to begin with, hence the association with high ISO and noise.
Noise is also introduced when trying to read the analogue signal. By amplifying before reading you add a small amount of read noise to a big signal, with little effect. By shooting at a lower ISO (keeping the other settings the same) you amplify less, to you add a small amount of read noise to a small signal, giving you a worse result by lowering ISO.
Reducing read noise by upping the ISO will help, but the primary problem you have is lack of light. You need to get more light down the lens, by either opening the aperture, or increasing the exposure time.
If increasing the exposure time/aperture causes other parts of the scene to be too bright (to the point where they show up pure white) then you have an additional problem that the dynamic range (the difference between the brightest and darkest parts) of the scene is too high, this can be fixed by using graduated filters, or by combining multiple exposures.
If you have a static(ish) scene I would recommend shooting several identical 25s exposures and then averaging them in software to reduce the noise. This is analogous to having one very long exposure, except without problems due to overexposure of certain areas. This is how most good DSLR astrophotography is done.