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public static void main(String[] args) {
 int m = askInt("Enter the value of M: ", 100, 10000),
 n = askInt("Enter the value of N: ", 1, 100);
 int solution = findSolution(m, n);
 System.out.println("Minimum number is: " + solution);
 System.out.println("Total number of digits: " + numberOfDigits(solution));
}

• Your program isn't object-oriented anyway, so there's no point in instantiating a and calling input() as an instance method. (Furthermore, it's weird that input(), which is an instance method, stores its results in static variables instead of instance variables.)
• There is a lot of repetition within input(). A general-purpose integer-prompting routine, used for both M and N, would be better.
• m, n, and ndigit should not be static variables, as that makes them essentially global variables. Any function in the class can alter their values as a side-effect, making your code harder to analyze — you have to read all of the code to understand any of it.

static int sumOfDigits(int num) {
 int sum = 0;
 while (num > 0) {
 sum += num % 10;
 num /= 10;
 }
 return sum;
}
static int numberOfDigits(int num) {
 return (int)Math.log10(num) + 1;
}

public static int findSolution(int m, int n) {
 for (int i = m + 1; ; i++) {
 if (sumOfDigits(i) == n) {
 return i;
 }
 }
}

public static void main(String[] args) {
 int m = askInt("Enter the value of M: ", 100, 10000),
 n = askInt("Enter the value of N: ", 1, 100);
 long solution = findSolution(m, n);
 System.out.println("Minimum number is: " + solution);
 System.out.println("Total number of digits: " + numberOfDigits(solution));
}

• Your program isn't object-oriented anyway, so there's no point in instantiating a and calling input() as an instance method. (Furthermore, it's weird that input(), which is an instance method, stores its results in static variables instead of instance variables.)
• There is a lot of repetition within input(). A general-purpose integer-prompting routine, used for both M and N, would be better.
• m, n, and ndigit should not be static variables, as that makes them essentially global variables. Any function in the class can alter their values as a side-effect, making your code harder to analyze — you have to read all of the code to understand any of it.
• The solution needs to be a long, in case N is large. As @OleTange pointed out, if N is 99, then the solution must be at least 99999999999, which won't fit in an int. Note that brute-force enumeration is a very poor strategy for such large numbers.

static int sumOfDigits(long num) {
 int sum = 0;
 while (num > 0) {
 sum += num % 10;
 num /= 10;
 }
 return sum;
}
static int numberOfDigits(long num) {
 return (int)Math.log10(num) + 1;
}

public static long findSolution(int m, int n) {
 for (long i = m + 1; ; i++) {
 if (sumOfDigits(i) == n) {
 return i;
 }
 }
}

• Your program isn't object-oriented anyway, so there's no point in instantiating a and calling input() as an instance method.
• There is a lot of repetition within input(). A general-purpose integer-prompting routine, used for both M and N, would be better.
• m, n, and ndigit should not be static variables, as that makes them essentially global variables. Any function in the class can alter their values as a side-effect, making your code harder to analyze — you have to read all of the cod to understand any of it.

• Your program isn't object-oriented anyway, so there's no point in instantiating a and calling input() as an instance method. (Furthermore, it's weird that input(), which is an instance method, stores its results in static variables instead of instance variables.)
• There is a lot of repetition within input(). A general-purpose integer-prompting routine, used for both M and N, would be better.
• m, n, and ndigit should not be static variables, as that makes them essentially global variables. Any function in the class can alter their values as a side-effect, making your code harder to analyze — you have to read all of the code to understand any of it.