I often heard analysts arguing that large increases like this are rarely followed by a productivity increase of the same amount and that it might even make some investors leave the country.
This sounds very vague. Many economic policies (higher taxes, lower spending, more debt, ...) have the potential to make some investors leave the country and there are always some analysts predicting imminent doom as consequence of almost any proposed policy.
When Germany introduced a minimum wage in 2015, quite a few prominent economics' scientists predicted the loss of in the order of hundreds of thousands of jobs. They erred and the unemployment continued to fall and the number of jobs continued to rise.
One positive effect of a higher minimum wage is that almost all of it is spent immediately and returned to the economy. So if indeed not too many people lose jobs through it, then there is also a chance of additional economical growth. Low incomes are spent proportionally more on domestic products (not spending money on expensive oversea-trips, buying second-hand cars instead of imported cars). There is a long going international trend of a declining wage share. An increased minimum wage could counteract the decline in the wage share and reduce inequality. A higher minimum wage is not only a risk but also a chance.
I wonder why having such a large increase at once and not increasing by a smaller percentage often (e.g. yearly). Theoretically, such a strategy should minimize the risks.
It would minimize the risk, but it would also minimize the chances. And it just may be a too small step anyway to show any effect.
Let's just assume for a moment that there is an optimal minimal wage, which might be defined as the minimal wage with the highest benefits (more income to lowly paid employees) at the lowest costs (less income to those not having jobs anymore).
Now the question is how far the current minimal wage is away from that optimal minimal wage. If the difference is large, then you actually want to make a large jump. 736€ per month doesn't sound like it's overly large, even 900€ per month doesn't sound like it's overly large, even more may be imaginable. For comparison, the minimum wage per hour in Germany is currently at 8.8€ which means something like (160 hours per month x 8.8€ per hour = 1408€ per month (before deductions), similar to the minimum wage in France) which is way above the numbers you have given for Spain.
Example: if the current minimal wage is $1 per month and the optimal minimal wage is $100 per month then you want to increase the minimum wage by 10,000 % and nothing less. It all depends on where you come from and where you want to go and what you fear more (over- or undershooting your goals).
I agree that once you are close to the optimal minimum wage you probably want to adjust the minimum wage in smaller steps.
How will we know if the rather large jump now was right or wrong? The time evolution of the unemployment/employment rate as well as the growth/shrinking of GDP will probably give a hint.
The current economic situation of Spain is not too bad. GDP is growing continuously since 2014 and unemployment is falling. However, unemployment is still quite high. A strong increase in the minimum wage might indeed be too risky. But that's far from sure. I think that the answer from Alex framing the strong increase as a pure election present is not proven sufficiently. I cannot exclude that the two major political parties supporting the increase in the minimum wage (PSOE and Podemos) actually believe this increase is a sound economic policy. Time will tell but it might be that the strong increase now will actually be beneficial for the Spanish economy.