Yes, there is caffeine in matcha. As it is a green tea there is caffeine, although the levels are almost half than that of coffee.
There is 34mg of caffeine per 1gram (1tsp) of matcha compared to 60-80mg of caffeine per 1gram of instant coffee.
Better Health recommend no more than 400mg of caffeine per day for adults. This includes caffeine in tea, coffee, energy drinks, chocolate and cola drinks. Pregnant women are advised to limit their caffeine intake.
If you are unsure please consult a health professional.