Are you using a font that has a proprietary encoding, or is it a Unicode font? I only ask because I don't recognize the script, at all… which is unusual, I thought I could identify any living language by eyeballing a few glyphs. 
If you don't know what I mean, just select any one glyph in InDesign, then go to Type -> Glyphs. Your one highlighted glyph will show up; if you mouse over it, a popup should identify the glyph name. If the glyph is not named correctly in that mouseover popup, then you are using some kind of non-Unicode font. In that case, I'd suggest looking at the kerning setting and making sure that it's not set to Optical. If you're using an old-fashioned proprietary-encoding font, then you'll mouse over a glyph and it will say something like “LATIN CAPITAL A WITH DIAERESIS.” InDesign will follow suit by treating your supposed-to-be-combining glyph as an a-with-diaeresis, which will generate spurious spaces.
Lastly, in case this is not helpful: please do post again with more details. What's the name of the font you are using? Do these ligatures work correctly in other OpenType-aware applications? And please, please do tell us what language that is!
Edited (for typos)