The company, previously named Kazakhmys, reduced its full-year cost guidance to 260-280 cents per pound, citing the weakening of the tenge and a better than expected performance from its mines in the east of Kazakhstan.
The tenge had been softening against the dollar even before this week's events. Kazakhstan also devalued its currency by almost 20 per cent in February 2014.
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Kaz Minerals, a constituent of the FTSE 250, rose 20 per cent in early morning trading on Thursday as analysts said the company would probably have to revise its cost guidance lower again later in the year. The shares were trading up 12 per cent at 13:00 UK time at 174.2p.
Analysts at Macquarie suggested Kaz Minerals may reduce its guidance again by as much as 11 per cent after this week's currency moves, which have pushed the tenge 24.5 per cent lower against the dollar this week.
The surge in Kaz Minerals'shares followed a 6.5 per cent jump on Wednesday, when Kazakhstan's central bank in effect devalued the tenge, a day before scrapping the band against the dollar altogether.
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It comes as other mining stocks suffering from the continuing fall in commodity prices. This week copper fell to a six-year low below $5,000 a tonne.
Kaz Minerals last year hived off its older mines into a new vehicle Cuprum Holding, led by its biggest shareholder, Vladimir Kim. The company now operates five mines compared with 16 before the restructuring, which was completed in October last year.
A number of countries with close trading links to China have been devaluing their currencies since last week, among them Vietnam.
Kazakhstan is heavily dependent on oil while the country remains closely tied to the recession-hit Russian economy, where the rouble has dropped 46 per cent against the dollar over the past 12 months.