In fact it works the other way - if you have high interest rates - it means people expect your currency to lose value. It's one of the less intuitive facts about currency, and the reason I'm happy I took economy course even though I dropped out of it on 4th year :)
The reason is - in "perfect knowledge world" it shouldn't matter if you keep your money for a year on bank account in country X, or if you instead change them into currency Y today, and keep it in country Y for a year (different interest rates), and then change them back to currency X.
If these 2 scenarios produce different outcomes - it means one of the banks is paying people more than it has to - contradiction in terms if I've ever seen one :)
So:
moneyInX * (1+interestRateX) = moneyInX * exchangeRateXToYToday * (1+interestRateY) / (exchangeRateXToYAfterAYear)
exchangeRateXToYAfterAYear = exchangeRateXToYToday*(1+interestRateY)/(1+interestRateX)
BTW that's what's happening in Russia now - high interest rates, recession, and currency losing value.
EDIT: but you're right that it could be caused by low growth, just the low-high interest rates mediation isn't there.