The math package has a constant for this and similar values, just use that: math.SmallestNonzeroFloat64:

const (
    MaxFloat32             = 3.40282346638528859811704183484516925440e+38  // 2**127 * (2**24 - 1) / 2**23
    SmallestNonzeroFloat32 = 1.401298464324817070923729583289916131280e-45 // 1 / 2**(127 - 1 + 23)

    MaxFloat64             = 1.797693134862315708145274237317043567981e+308 // 2**1023 * (2**53 - 1) / 2**52
    SmallestNonzeroFloat64 = 4.940656458412465441765687928682213723651e-324 // 1 / 2**(1023 - 1 + 52)
)

Printing its value:

fmt.Println(math.SmallestNonzeroFloat64)

Outputs (try it on the Go Playground):

5e-324

(Note: it's greater than the constant due to rounding in the fmt package.)

For example,

package main

import (
    "fmt"
    "math"
)

func main() {
    const f = math.MaxFloat64
    fmt.Printf("%[1]T %[1]v\n", f)
    const c = complex(math.MaxFloat64, math.MaxFloat64)
    fmt.Printf("%[1]T %[1]v\n", c)
}

Output:

float64 1.7976931348623157e+308
complex128 (1.7976931348623157e+308+1.7976931348623157e+308i)

Package math

import "math" 

Floating-point limit values. Max is the largest finite value representable by the type. SmallestNonzero is the smallest positive, non-zero value representable by the type.

const (
        MaxFloat32             = 3.40282346638528859811704183484516925440e+38  // 2**127 * (2**24 - 1) / 2**23
        SmallestNonzeroFloat32 = 1.401298464324817070923729583289916131280e-45 // 1 / 2**(127 - 1 + 23)

        MaxFloat64             = 1.797693134862315708145274237317043567981e+308 // 2**1023 * (2**53 - 1) / 2**52
        SmallestNonzeroFloat64 = 4.940656458412465441765687928682213723651e-324 // 1 / 2**(1023 - 1 + 52)
)

The Go Programming Language Specification

Numeric types

A numeric type represents sets of integer or floating-point values. The predeclared architecture-independent numeric types are:

uint8       the set of all unsigned  8-bit integers (0 to 255)
uint16      the set of all unsigned 16-bit integers (0 to 65535)
uint32      the set of all unsigned 32-bit integers (0 to 4294967295)
uint64      the set of all unsigned 64-bit integers (0 to 18446744073709551615)

int8        the set of all signed  8-bit integers (-128 to 127)
int16       the set of all signed 16-bit integers (-32768 to 32767)
int32       the set of all signed 32-bit integers (-2147483648 to 2147483647)
int64       the set of all signed 64-bit integers (-9223372036854775808 to 9223372036854775807)

float32     the set of all IEEE-754 32-bit floating-point numbers
float64     the set of all IEEE-754 64-bit floating-point numbers

complex64   the set of all complex numbers with float32 real and imaginary parts
complex128  the set of all complex numbers with float64 real and imaginary parts

byte        alias for uint8
rune        alias for int32

The value of an n-bit integer is n bits wide and represented using two's complement arithmetic.

There is also a set of predeclared numeric types with implementation-specific sizes:

uint     either 32 or 64 bits
int      same size as uint
uintptr  an unsigned integer large enough to store the uninterpreted bits of a pointer value

To avoid portability issues all numeric types are distinct except byte, which is an alias for uint8, and rune, which is an alias for int32. Conversions are required when different numeric types are mixed in an expression or assignment. For instance, int32 and int are not the same type even though they may have the same size on a particular architecture.

Starting with Go 1.21, min and max are available as builtins and you do not need to write them at all. (Thanks @ufukty for highlighting this in a comment.)

I'm leaving the previous content below in case someone needs a different simple generic function that isn't built in or can otherwise use the historical answers.

Until Go 1.18 a one-off function was the standard way; for example, the stdlib's sort.go does it near the top of the file:

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}

You might still want or need to use this approach so your code works on Go versions below 1.18!

Starting with Go 1.18, you can write a generic min function which is just as efficient at run time as the hand-coded single-type version, but works with any type with < and > operators:

func minT constraints.Ordered T {
    if a < b {
        return a
    }
    return b
}

func main() {
    fmt.Println(min(1, 2))
    fmt.Println(min(1.5, 2.5))
    fmt.Println(min("Hello", "世界"))
}

There's been discussion of updating the stdlib to add generic versions of existing functions, but if that happens it won't be until a later version.

math.Min(2, 3) happened to work because numeric constants in Go are untyped. Beware of treating float64s as a universal number type in general, though, since integers above 2^53 will get rounded if converted to float64.